In identical statements released yesterday, it was said that the two leaders met in Killarney to discuss a range of issues.
The meeting was expected as part of a review of the deal, by which Fianna Fáil facilitates the Fine Gael minority government from the opposition benches.
Relations between the two parties have chilled in recent weeks.
Earlier this month, the two men exchanged verbal blows, amid heightened talk of a possible early election in September.
Mr Martin has repeatedly resisted suggestions from Mr Varadkar to enter into talks about extending the deal ahead of the budget.
He has said his preference is to wait until after the budget, before opening discussion.
Mr Varadkar has argued, for the sake of stability, that such talks should commence earlier than that.
Last week, the Taoiseach, through his chief of staff, Brian Murphy, extended an invitation to Mr Martin to meet to review the deal and that offer was accepted.
This week, the Taoiseach told a specially covened Cabinet meeting in Derrynane, Co Kerry, that he would seek a two-year extension to the deal from Mr Martin.
It is understood the two men met on Thursday evening for over an hour.
The statements said: “Fine Gael party leader, Leo Varadkar, has met with Fianna Fáil leader, Micheál Martin. The party leaders met in Killarney, as agreed, and had a constructive discussion on a range of issues.”
The matters discussed included Brexit, the forthcoming budget, the upcoming referenda and the confidence-and-supply arrangement, the parties said.
“They shared with one another their perspectives on all of these matters,” the statements added. But it is clear the meeting ended without resolution, as they have agreed to meet again after the summer recess.
“Leo Varadkar gave his views about the need to review and renew the confidence-and-supply arrangement. Micheál Martin reiterated his view that, as per the confidence-and-supply arrangement, a review is provided for at the end of 2018,” the statements said.
“The leaders agreed to meet again in early September. Both parties will also engage, in the meantime, on the forthcoming budget,” the parties said.
Earlier this month, Mr Martin branded Mr Varadkar a “prickly” man “with an authoritarian streak”.