Minister for Health Simon Harris said it was hard and galling to take a lecture from the Fianna Fáil leader on health spending.
Micheál Martin has claimed that the Government has failed to reveal the full truth around health spending for the last three budgets.
He said this was because not enough was provided at the beginning of each year for elderly services.
Minister Harris said that when Mr Martin was health minister, he could have stopped illegal nursing home charges but failed abysmally.
He also said, that at the Cabinet table, Mr Martin took thousands of medical cards from people over 70.
Minister Harris said that his Government was increasing and expanding investment in health.
Responding to the minister's comments, Mr Martin said Mr Harris had failed to rebut the claim that health spending budget figures had been fraudulent for the last three years.
Mr Martin also accused Mr Harris of being a poor and ineffective health minister.
Fianna Fáil has called for full transparency on health spending as Budget talks between the party and the Minister for Finance get under way.
The Fianna Fáil parliamentary party meeting concludes today in Gorey, Co Wexford ahead of the resumption of the Dáil next week.
Micheal Martin: We've negotiated 3 budgets in good faith, the overarching focus has been service. The health service is imploding. Access is very difficult for too many people .— Morning Ireland (@morningireland) September 10, 2019
The discussions take place against the backdrop of Fine Gael accusing Fianna Fáil of making spending calls that run to billions.
In response, Fianna Fáil has focused on Government overspending and in particular the initial failure to accurately calculate the cost of building the new National Children's Hospital.
Speaking on RTÉ's Morning Ireland, Mr Martin said the the health service was imploding and he wanted to ensure that people had the resources to get access to the services that they need.
He also said he believed that a carbon tax should be introduced and money raised from this tax should be ring-fenced to fund activities under climate change and biodiversity.
Mr Martin said while there cannot be an election if the prospect of a no-deal Brexit remains on the horizon, there would be a vote in 2020 and believed there will be a fragmented Dáil following the next general election.
War of words between Health Minister and FF Leader continues. M Martin sticking by his claim that budget health figures were "fraudulent" over 3 years and says Simon Harris has not been a good minister. @rtenews pic.twitter.com/P3thgIXFh9— Mícheál Lehane (@MichealLehane) September 10, 2019
Reporting Micheál Lehane & Fergal Bowers