Minister for Social Protection Regina Doherty has described Fianna Fáil's response Taoiseach Leo Varadkar's letter as "childish".
Ms Doherty also said that Fine Gael would not take no for an answer "we're going to keep trying."
Taoiseach Leo Varadkar published a letter yesterday that he had sent to Fianna Fáil leader Micheál Martin last week arguing for an extension of the confidence-and-supply agreement and seeking immediate negotiations between the two parties.
Mr Martin rebuffed Mr Varadkar's appeal for talks on an extension of the agreement for up to two years, saying he would enter talks only towards the end of the year, as specified in the original agreement.
Talks between the two parties on this year’s budget – due to be delivered on October 9th – are to begin today.
Under the confidence-and-supply arrangement, agreed between Fine Gael and Fianna Fáil after the 2016 election, Fianna Fáil facilitates the Fine Gael-led minority Government by abstaining in Dáil votes including on the Budget every year.
Fianna Fáil also agreed under the deal to vote against or abstain on any motions of no confidence in the Government. The arrangement is due to be reviewed at the end of 2018, but Mr Varadkar has sought talks with Fianna Fáil to agree an extension of the agreement. (What did the confidence-and-supply arrangement include?Explainer here)
Ms Doherty said Fine Gael were trying to “negotiate a contract before the contract runs out”.
“You don’t leave a contract until its dying days before you start renegotiating,” she said.
“That’s all we want to do here. There’s no tactics, no stunts, there’s no nothing.”
Ms Doherty told RTÉ's Morning Ireland all parties have agreed an election was not wanted.
“Fianna Fáil doesn’t want an election, Fine Gael and the Independents don’t want an election, I don’t think the Irish people want an election. Let’s park that,” she said.
“The two courses of action are not mutually exclusive, I don’t understand why we can’t pursue the two of them in parallel, I don’t understand the vehement objection so quickly yesterday.”
The Minister said there was an “underlying tone” from Fianna Fáil that “if they don’t get what they want then they will cause an election.”
Ms Doherty said there was a need for strength of purpose in relation to the Brexit negotiations and “the only way we can do that is with certainty that the parliament has longevity. That it has stability.
"We will do the negotiations this year, they were seamless last year. Dara Calleary, Michael McGrath were utter professionals last year, no doubt there's going to be exactly the same this year - we will deliver for the Irish people.
"I don't see the harm in asking Fianna Fáil to sit down to review what has been a good contract for the last number of years with a view to continuing that contract in what has been an uncertain time for the island of Ireland. "
She said that the Taoiseach’s letter is not an election manifesto. “It is a work programme of what we want to achieve between ourselves and Fianna Fáil in the next 12 - 18 months. The reason the letter was published was in an air of transparency so there would be no accusation of leaking, spinning stuff, this is just being honest and open.
“Putting on the record, on the table, this is what we want to do. What we would like to see for the future of Ireland.
Earlier on Wednesday, Fianna Fáil’s finance spokesman Michael McGrath has described Taoiseach Leo Varadkar’s calls for discussions on the confidence and supply agreement as “some form of manoeuvre, a political tactic.”
“It doesn’t strike me as a genuine attempt to get talks under way. There’s something else to it. I don’t know,” he told RTÉ’s Morning Ireland.
Mr McGrath said that his party was more interested in the outcome of the third Budget negotiations.
There is “unfinished business” in the Confidence and Supply agreement in the areas of housing and health, Mr McGrath said.
“We want delivery of an affordable housing scheme.”
He said there had not been sufficient movement on matters such as early assessment for special needs children, prevention services and additional home care packages.
“There is still a third of the existing agreement to go. The actual Budget is the centre piece of the agreement.”
Delivery of items in the Budget is going to be part of the overall assessment.
“We were here for the passage of two Budgets, we got on with our business with no fanfare.”
Mr McGrath said he questioned Mr Varadkar’s motivation.
When asked if Fianna Fáil was ready for an election, he said as a political party they were always ready and did not fear an election.
Minister for Agriculture Michael Creed rejected Fianna Fáil's suggestions that Taoiseach Leo Varadkar might be trying to force an early election with the letter sent to Fianna Fáil leader Micheal Martin requesting talks on a new confidence and supply deal.
Speaking at a conference on Brexit’s impact on the agri-food sector, Mr Creed said Mr Varadkar urgently wanted a deal to keep the minority Fine Gael-led government in power until 2020.
“Fine Gael doesn’t want an election, the Government doesn’t want an election and the last thing the country needs in the context of all of this ongoing debate around Brexit and other issues is an election,” Mr Creed told The Irish Times.
“We want to negotiate as soon as possible and that is clearly what the Taoiseach’s intention is.”