Anything less than full mandatory 14-day quarantine for all travellers entering Ireland would be "absolutely insufficient", Mary Lou McDonald has said.
The Sinn Féin president has hit out at the "laissez-faire" and "hit and miss" approach that has so far been taken by the Government to travellers arriving here from abroad.
Pointing to the fact that many people have been out of work for almost a year now, she said: "I think now at this juncture is absolutely proportionate to ensure that those coming onto the island are tested pre-arrival, tested post-arrival, and that the quarantine isn't laissez-faire."
She said "very firm and very secure arrangements" must be introduced to make sure all passengers fully comply with 14-day quarantine requirements.
"I would be urging the Government to move away from any kind of minimalist notion that quarantine is only for those who arrive without their negative test. It needs to be much more comprehensive than that."
The Cabinet sub-committee on Covid is due to meet today to discuss introducing mandatory quarantine for those who arrive here without a negative PCR test.
It is expected that the committee will also discuss the reopening of schools and the continuation of level 5 restrictions.
Ms McDonald said for measures to work they must be introduced island-wide and added that gardaí and the PSNI have the power to turn people back if they are travelling further than 5km.
"Any idea that you can corral the virus into a corner of the island and keep the rest of us safe is very very sadly misinformed, that's not the case, if there's a reservoir of this virus anywhere on our island it places all of us in danger."
She said there is "no rational basis" for closing the border between North and South but said, "nobody should be travelling anywhere unless it is absolutely essential".
She told RTÉ's Morning Ireland programme that the Taoiseach must now go "beyond making a couple of phone calls" and work with the Executive in Northern Ireland on developing the same restrictions across the island.