Fianna Fáil has accused the Taoiseach of trying to provoke an election by making claims that are not true.
The party is insisting that it "will not rise to the bait" and will only review the Confidence and Supply Agreement after the Budget in October.
A spokesperson for Leo Varadkar has said they will not get involved in a tit-for-tat with Fianna Fáil and described earlier comments from Micheál Martin as "personalised attacks".
Mr Martin had reacted to comments made by the Taoiseach that Fianna Fáil was giving mixed messages about its position on the confidence and supply deal.
In a tweet, Mr Martin stated: "Why is the Taoiseach Leo Varadkar persisting with dishonest, provocative comments re my party's position?
"We have been very very clear that we want to negotiate 3rd budget in country's interest and at no stage did we say we'd be supporting SF's Phantom Confidence Motion stunt."
The parties are clearly at odds about when the key agreement underpinning the minority Government must be reviewed.
It is understood that Fine Gael are adamant that discussions at least must begin before the Budget.
However, this has been categorically rejected by Fianna Fáil.
Much focus is now likely to turn to when the Taoiseach and the Fianna Fáil leader next meet.
A spokesperson for Mr Varadkar said that an approach would be made to Mr Martin at the "appropriate time".
They said: "As the Taoiseach clearly stated earlier, the Government has no intention of getting into a tit-for-tat with Fianna Fáil.
"Our focus is on running the country, improving essential services for families, raising living standards and encouraging economic growth."