Minister for Health Simon Harris has said negotiations with Fianna Fáil on an extension to the confidence and supply agreement should start before the Budget.
Mr Harris said this would provide certainty about what would happen once the Budget was passed.
"It is a statement of fact that the confidence and supply agreement will come to an end this year, therefore it is timely to have that conversation ... to decide what happens next," he said.
"We cannot have a situation where the country falls off a cliff in terms of Government. It is my view, that it makes sense that that conversation would take place before the Budget."
Responding to comments from Fianna Fáil leader Micheál Martin - who said the Taoiseach should call an election if he wanted one - Mr Harris said: "I think the heat must be getting to the leader of the Fianna Fáil party.
"I think he needs to calm down now, the Government doesn't want an election, the Government wants to get on with the job of governing.
"It is unfortunate that when the Taoiseach is out of the country representing Ireland, that the opposition persists in what are partisan attacks"
Earlier, Mr Martin said the Taoiseach should call a general election if he wanted one.
He said Mr Varadkar had created "hype" around an election by "falsely" suggesting that Fianna Fáil may support a Sinn Féin motion of no confidence in Minister for Housing Eoghan Murphy.
Speaking on Newstalk, Mr Martin said: "Maybe he wants an election, if he wants an election, let him call an election".
Addressing the prospect of an early election, Mr Martin said: "The Taoiseach himself created the hype, and I think the Taoiseach has contributed to all of this, in the sense that he has raised the spectre falsely about us openly talking about supporting a Sinn Féin motion that was never tabled, it was a phantom motion, it was a bit of a stunt at the time.
"Sinn Féin talked it up in advance of their ard fheis, Leo Varadkar talked it up, maybe he wants to have an election, if he wants an election let him call an election."
The Independent Alliance has said it supports comments by Mr Martin that there should be no election in the immediate future.
Members of the Alliance said it was imperative that there was stability in Government while talks enter a critical phase in the Brexit negotiations.
A spokesperson said: "Speculation of a autumn general election must be put aside for the sake of the country."
"Now is not the time to be talking of snap general elections while the economy continues to improve across all sectors."
Tanáiste Simon Coveney has said it was time to "tone down the rhetoric" about an election and "get on with the job".
Speaking on RTÉ’s Today with Séan O'Rourke, he said the Taoiseach would like to see early discussions about the "continuation or not" of the confidence and supply agreement so decisions could be made "in the interests of the country".
"The Government will have to make decisions in the interest of the country.
"We don't want an election, I don't think the country wants an election, they want us to get on to face the challenges."