The motion has been put forward by the main opposition Fianna Fail party, which has propped up Varadkar's Fine Gael minority government since an inconclusive general election in 2016.

The crisis comes just as Ireland is trying to extract guarantees from Britain that its border with British-ruled Northern Ireland will remain open even after Brexit ahead of a crucial EU summit next month.

Britain has said it wants to leave the EU's single market and customs union when it quits the EU, which could mean customs checks along the Irish border.

Ireland has asked for Northern Ireland to be granted a special customs status to keep the border open but Britain says this would create a new border between Northern Ireland and the rest of Britain.

The issue will top the agenda for the December 14-15 summit in Brussels which is due to decide whether or not to begin negotiations with Britain on a possible post-Brexit transition period and future trade ties.

Whistleblower scandal

The domestic political crisis in Ireland has been brewing ever since a police whistleblower scandal dating back to 2015 and centres on Deputy Prime Minister Frances Fitzgerald's role at the time.

Fianna Fail leader Micheal Martin and Varadkar have been meeting daily since Thursday and, while their tone has moderated, there seems to be no way out of the crisis as the prime minister has refused to sack Fitzgerald.

Fianna Fail's justice affairs spokesman Jim O'Callaghan was equally trenchant after talks on Monday: "Our position has not changed. She should go."

Fianna Fail MP Michael McGrath said his party wanted to compromise, but also sounded a warning.

"It is our objective to avoid an election but not at the price of discarding the requirements for political accountability," he said.

Fitzgerald has said she will give evidence to a judicial inquiry into the case but will not step down despite pressure from some Fine Gael deputies.

Varadkar was due to meet Martin again on Tuesday.

"We are trying to find a middle way that allows the government to continue and continue with the important work we are doing in particular in relation to Brexit and ensuring that we have the necessary legislation in place," Varadkar said on Monday.

According to the latest poll by Red C for the Sunday Business Post, Fine Gael would get 27 percent of the vote, followed by Fianna Fail on 26 percent and Sinn Fein on 16 percent, raising the prospect of another minority government even after elections.