Leaders of the world's biggest economies are in the Chinese city of Hangzhou for the annual G20 summit.
The annual G20 summit opens shortly in the Chinese city of Hangzhou, after a series of bilateral meetings to discuss regional security, Syria, trade and climate change.
It is the first time China has hosted the summit. The health of the global economy will be high on the agenda.
UN secretary general Ban Ki Moon warned sluggish recovery from the global financial crisis still threatened smaller countries.
China is keen to ensure a smooth summit, its highest-profile event of the year, as it looks to enhance its global standing and avoid acrimony over a long list of tensions with Washington.
Some G20 leaders have already begun drawing battle lines in disputes over issues like trade and investment, tax policy, and industrial overcapacity.
Security is extremely tight in Hangzhou, with parts of the city of 9,000,000 people turned into a virtual ghost town as China seeks to ensure that the G20 summit is incident-free.
The G20 group includes Argentina, Australia, Brazil, Canada, China, France, Germany, India, Indonesia, Italy, Japan, South Korea, Mexico, Russia, Saudi Arabia, South Africa, Turkey, the United Kingdom and the United States along with the European Union.
New Zealand is not a member and is not attending the summit.
US and China meeting off to rough start
Mr Obama said on Sunday his talks with his Chinese counterpart Xi Jinping a day earlier had been "extremely productive" and the significance of a row between US and Chinese officials at the airport upon his arrival should not be overblown.
Mr Obama's last scheduled trip to China before leaving office got off to an awkward start soon after Air Force One landed in Hangzhou when a Chinese security official blocked National Security Adviser Susan Rice on the tarmac and yelled at another US official trying to help journalists get closer to Mr Obama.
"I wouldn't overcrank the significance" of tensions at the airport, Mr Obama told a news conference, where global leaders are convening for a G20 summit.
Arriving on Saturday, Mr Obama held talks with Mr Xi that ran late into the night. He urged Beijing to uphold its legal obligations in the disputed waters of the South China Sea, and stressed US commitments to its regional allies.
Mr Xi said China would continue to safeguard its sovereignty and maritime rights in the South China Sea, according to a statement on the Chinese foreign ministry's website.
The two leaders and their delegations met for over four hours before Mr Obama and Mr Xi talked one-on-one as they took a night-time stroll.
Tensions over the disputed waters between China and its neighbors were expected to hang over the summit, with host city Hangzhou on China's east coast.
Mr Obama, now in the last five months of his presidency, wanted to put a final stamp on his signature policy shift toward the Pacific, setting the tone for his White House successor who will be elected in November and take office on 20 January.
He has invested in developing closer ties with nations in Southeast Asia, and is taking pains in his last scheduled trip to the region to reassure partners worried about the economic and military might of China.
After the meetings with Mr Xi and his top officials, Mr Obama emphasized the importance for China to "abide by its obligations" to an international maritime treaty in the dispute over rights to a territory rich in oil and fish through which $5 trillion in trade travels each year.
An arbitration court in The Hague ruled in July that China had no historic title over the waters of the South China Sea and had infringed on the rights of the Philippines, which brought the case under the U.N. Convention on the Law of the Sea.
China, India move towards closer relations
Meanwhile Mr Xi told Indian Prime Minister Narendra Modi on Sunday the two countries should respect each other's concerns and constructively handle their differences.
The two nuclear-armed neighbours have been moving to gradually ease long-existing tensions between them.
Leaders of Asia's two giants pledged last year to cool a festering border dispute, which dates back to a brief border war in 1962, though the disagreement remains unresolved.
Meeting on the sidelines of the G20 summit, Mr Xi said relations had maintained a steady, healthy momentum, and should continue to increase mutual understanding and trust.
"We ought to respect and give consideration to each other's concerns, and use constructive methods to appropriately handle questions on which there are disputes," Mr Xi said in comments carried by China's Foreign Ministry.
"China is willing to work hard with India the maintain the hard-won good position of Sino-India relations," Mr Xi said.
China's Defence Ministry said last month that it hoped India could put more efforts into regional peace and stability than the opposite, in response to Indian plans to put advanced cruise missiles along the disputed border with China.
Indian military officials said the plan was to equip regiments deployed on the China border with the BrahMos missile, made by an Indo-Russian joint venture, as part of ongoing efforts to build up military and civilian infrastructure capabilities there.
China lays claim to more than 90,000sq km ruled by New Delhi in the eastern sector of the Himalayas. India said China occupied 38,000sq km of its territory on the Aksai Chin plateau in the west.
India is also suspicious of China's support for its arch-rival, Pakistan.
Mr Modi arrived in China from Vietnam, which is involved in its own dispute with China over the South China Sea, where he offered Vietnam a credit line of $US500,000 for defence cooperation.
Mr Modi's government has ordered BrahMos Aerospace, which produces the BrahMos missiles, to accelerate sales to a list of five countries topped by Vietnam, according to a government note viewed by Reuters and previously unreported.
US missiles in South Korea
But the South China Sea and India were not the only borders China was concerned about leading up to the summit.
South Korea's President Park Geun-hye is set to meet Mr Xi on Monday, South Korea news agency Yonhap reported on Sunday, citing Park's office.
The two would be meeting after a period of tension between them caused by a decision by South Korea and its ally, the United States, to deploy an advanced anti-missile system in South Korea to counter North Korea's growing missile capability.
China opposes deployment of the Terminal High Altitude Area Defense (THAAD) system, saying it could undermine security in the region.
Brexit looms large for Europe and beyond
Speaking before travelling to China for the G20 summit in her first major interview since taking office, UK Prime Minister Theresa May warned Brexit would not be "plain sailing" for the UK.
She said formal EU talks will not begin until 2017, but vowed the process would not be "kicked into the long grass".
Mrs May also ruled out a snap general election, as the UK needs "stability".
The former home secretary became prime minister after David Cameron resigned in the wake of the EU referendum - with the Brexit process likely to dominate the first years of her premiership.
Ahead of the summit, she met for talks with US President Barack Obama.
Mr Obama told reporters at the Summit in China the US would "consult closely" with the UK over Brexit negotiations to ensure there were no "adverse effects" in the US-UK trading relationship.
"We're going to do everything we can to make sure that the consequences of the decision don't end up unravelling what is already a very strong and robust economic relationship that can become even stronger in the future," Mr Obama said.
Australian Prime Minister Malcolm Turnbull, also at the Summit on Sunday, said his country and Britain were both very committed to having an early free trade agreement after Britain leaves the European Union.
"Prime Minister May and I are very committed to having an early free trade agreement put in place so that when Britain leaves the EU, we have very open markets between Australia and Britain," Mr Turnbull said.
"They've got to put in place free trade agreements and we are enthusiastic and supportive; we're providing Britain with as much assistance as we can at a technical level," Mr Turnbull said.
Meanwhile, Mrs May also said ahead of meeting with Russian President Vladimir Putin she hoped for an open dialogue with Russia even though the two countries had serious differences.
"While I recognise there will be some differences between us, there are some complex and serious areas of concern and issues to discuss, I hope we will be able to have a frank and open relationship and dialogue," Mrs May said.
US, Russia in talks over Syrian conflict
Mr Obama also said the US and Russia were working on Sunday to try to finalize a ceasefire in Syria that would allow more deliveries of humanitarian aid in the war-torn country.
A deal could be announced as early as Sunday, a senior U.S. State Department official said.
"We're not there yet," Mr Obama told reporters after a meeting with Mrs May, noting previous ceasefires had failed to last for long.
Military officials from the US and Russia, which back opposite sides in Syria's five-year war, have been meeting for weeks to try to work on terms of a deal.
The civil war has killed more than 250,000 people and displaced 11 million, causing a refugee crisis in the Middle East and Europe, and contributing to a rise in militant Islamist groups.
"We have grave differences with the Russians in terms of both the parties we support but also the process that is required to bring about peace in Syria," Mr Obama said.
Russia has backed Syrian President Bashar al-Assad, but the United States has worked with moderate opposition forces fighting Assad.
"But if we do not get some buy-in from the Russians on reducing the violence and easing the humanitarian crisis, then it's difficult to see how we get to the next phase, he said.
The White House has said Mr Obama and Russian President Vladimir Putin likely would have the chance to talk informally on the sidelines of the G20. No time for that meeting has been announced.
- Reuters / BBC