Fianna Fáil leader Micheál Martin has written to the Taoiseach telling him that it would be best that they "both agree not to bring down the government".
Mr Martin said that they should state upfront that they are in agreement "in light of recent developments and as we head into this critical period on Brexit...irrespective of what happens during the Confidence and Supply review process".
Mr Martin also encouraged Leo Varadkar to agree on passing the Budget Finance Bill and other legislation at least until a Brexit agremeent has been reached by the UK and the EU.
"The Irish people would, I am sure you agree, be rightly concerned at any risk that a general election campaign would have on these talks at such a crucial period and an uncertain post-election situation," he wrote.
He said that an election during this "critical time would create a dangerous instability during a period when the Brexit deal could be derailed by the constantly changing situation in Westminster".
The two leaders were in contact this morning and have both agreed to meet next week.
Mr Martin said he is available to discuss the contents of the letter further with him if he wishes.
NEW: Micheál Martin has written to Leo Varadkar saying they should both agree not to bring down the government until a Brexit deal is in place pic.twitter.com/piJ741vMxr
— Seán Defoe (@SeanDefoe) October 12, 2018