The National Party wants to make it compulsory for people in managed isolation and quarantine facilities to be tested on day three of their stay.
Currently, it is only compulsory for testing on day 12, and the government has said that is enough to keep the public safe.
If a test was refused at this time, people would be forced to spend another 14 days in isolation.
However, National's health spokesperson Dr Shane Reti said this wasn't good enough.
"If you wait to day 12, you have all those days in managed isolation where you're mixing with cohorts, giving it to other people, giving it to staff," he said.
"We should just make it compulsory at day three like we do at day 12. If the test is refused at day three, then you become a presumed positive and you move through to quarantine. "
The proposal is one of five released by the National Party, which also included requiring people who test negative for Covid be notified within a 48 hours period so they can get back to work sooner.
Reti said he was aware of people waiting up to eight days to get a negative test result.
He also proposed re-testing every positive case within 24 hours to get better genomic data.