Minister for Health Stephen Donnelly has said he would not support restrictions on cross-border travel.
Mr Donnelly said he did not think the Covid-19 situation in border counties currently warranted the measure.
Last week, the North’s Health Minister Robin Swann wrote to Mr Donnelly calling for a halt to non-essential cross-border travel, insisting it should be done “by enforcement if required”.
The letter was written after recent surges in infection numbers in Donegal and across the border in the Derry city and Strabane council area.
Mr Donnelly said the spikes in Donegal were largely confined to two specific electoral areas and he said the infection rates were now on a downward trajectory again.
From Monday, a lockdown restriction preventing non-essential travel between counties will lift in the Republic.
“We have an open border, a very open border on the island,” Mr Donnelly told RTÉ Radio One.
“I don’t want to see that change, the Irish Government does not want to see that change. I believe that the island is doing very well, both north and south, at the moment and actually Donegal is doing quite well.”
Mr Donnelly said a formal response to Mr Swann was still being formulated by his officials. He said he would also be speaking with his northern counterpart next week about the issue.
“It’s a conversation we’ll have at government and obviously I’ll discuss it directly with Minister Swann,” he said.
“My own view right now is that the epidemiological situation wouldn’t warrant that, we are opening up to inter-county travel, we are not changing that tomorrow certainly.”