MARY LOU MCDONALD says that anyone arriving into Ireland should be forced to quarantine for two weeks.
The Sinn Féin leader stressed that enforcing such a rule is the only way to stamp out non-essential travel throughout the country.
"Nothing will act as a more effective pushback on travel that isn't essential than a mandatory quarantine for 14 days," she said on RTÉ's Morning Ireland.
McDonald added that the government's plan to only quarantine those who fail to produce a negative Covid-19 test was "insufficient".
"I'm very surprised at this stage that they don't realise this, especially with NPHET and other public health experts saying this," she added.
"We have to grasp this nettle now."
Ms McDonald went on to say that it was absolutely essential, given the current infection levels around the country, and the pressure hospitals are under as a result, that everyone is tested pre and post arrival in Ireland, so the quarantine rules aren't "hit and miss".
Cabinet is expected to announce a number of new measures on Tuesday including the aforementioned mandatory quarantine for anyone who fails to show proof of a negative Covid test.
They're also considering placing gardaí on the Northern Irish border to ensure that anyone entering Ireland from the North is adhering to the same rule as anyone arriving through airports.
McDonald insists though that the new measures are not substantial enough.
"Nobody should be coming onto the island of Ireland unless essential and when they come onto the island they should have a negative PCR test," she said.
"If they don't have a negative test, they should be sent back from whence they came. We should also have a second mandatory test after five days of being on the island."
