Taoiseach Leo Varadkar is promising tax cuts and increases to the state pension if Fianna Fail continues to prop up his Government until 2020.
However, a 10-page letter from the Fine Gael leader to Micheal Martin has sparked anger in the opposition party, which believes political games are being played.
In a forthright letter, Mr Varadkar told Fianna Fail the Government will not be able to function unless there is clarity about its longevity.
He said doubts over when the next election might be held would weaken Ireland's hand in Brexit negotiations.
"I'm writing to you to seek confirmation that you are willing to recommit to the confidence and supply arrangement for the remainder of this Dail," the letter states.
"I suggest that in the interest of certainty we agree a general election date for the summer of 2020."
Mr Varadkar said it is his "strong view" that a government cannot act in the best interests of the people "if it is living on borrowed time".
"A government cannot function if it does not know if it will last from week-to-week or month-to-month; if it does not know what will happen to its programme and legislative agenda the day after Budget Day or the day the Finance Bill is passed," he wrote.
"Such uncertainty weakens our hand in Brexit talks, domestic negotiations, and of course those opposed or resistant to reform are simply more likely to wait us out.
"Such a scenario would not be in the interest of citizens, taxpayers or users of our public services."
This assertion was shot down by Fianna Fail leader Mr Martin, who believes the Taoiseach is trying to spark an election.
"What's happening here is that the Taoiseach and Fine Gael party, for some reason, have upped the ante. They seem to want an election," he said.
In his letter, Mr Varadkar outlines why he believes Fine Gael has lived up to the unprecedented confidence and supply deal, which was struck more than two months after the 2016 election.
He admitted the Government is "struggling to make sustainable improvements to public healthcare".
"While there is now some cause for optimism, the housing crisis persists. Without doubt, there is more to do," he said.
Mr Varadkar added that the economy is "powering ahead at a much faster rate than projected and we are approaching full employment".
"There are now some concerns about overheating with growing downside economic risks due to international developments such as changes in the international corporation tax landscape and the possibility of disruptions to the global trading system," he wrote.
His pitch to Mr Martin includes a long but "not exhaustive" list of items he would like to form the basis of a renewed deal.
Under the heading "Prudent Management of the Public Finances", Mr Varadkar says there is a need to reduce the number of people who pay the top rate of income tax.
This would mean that a single person earning €40,000 would be paying €590 less annually by the time of Mr Varadkar's proposed 2020 general election.
The Taoiseach also commits to limiting property tax increases and to increase the state pension and weekly social welfare rates at or above the rate of inflation.
Mr Martin said he has given the Government "space and stability" in relation to Brexit so the Taoiseach's actions were "not good politics".
"I think it's putting the party before the country, in terms of Fine Gael," he said.
"If they want an election, that's their business, but they should be honest about it."
He insisted that talks on a new deal cannot begin until after Budget 2019 is presented to the Dail on October 9.
"There has to be respect and respect for the procedures and written agreement that's laid down," Mr Martin said.