Fianna Fáil leader Micheál Martin has warned that British-Irish relations have "deteriorated significantly" due to Brexit.
He called on the Taoiseach to desist from engaging in "childish" language which he said is making the situation worse.
Mr Martin was referencing comments made by Leo Varadkar last week at a Fine Gael gathering in which he said: "Westminster might be the mother of all parliaments but it's not the boss of other parliaments."
Speaking on RTÉ's The Week in Politics, Mr Martin said: "It's very childish kind of stuff that we don't need to be doing. It's getting too serious for that. It's a very serious issue."
He said that Britain was "in trouble politically" and there was "incoherence there".
He said: "But what we must do is to try and work with Europe, and with the British government, to make sure that their leaving Europe does not leave everyone poorer."
Mr Martin accused the Taoiseach of adopting an approach on Brexit which has "impacted so negatively on British-Irish relations, on North-South relations and polarised divisions in the community."
However, the political charge was rejected as being "both unfair and untrue" by Minister for Housing Eoghan Murphy.
He said the Taoiseach, along with Mr Coveney and Minister for European Affairs Helen McEntee have put in a "huge amount of work" to ensure that, despite the difficulties with Brexit, the Government was "enhancing and improving bilateral relationships all the time."
Mr Murphy said: "We are coming into a very important period for this country, for the Oireachtas as well - now is not the time to start politicising Brexit to any one party's political advantage."
Peace process cannot be compromised for Brexit deal
Earlier, Tánaiste and Minister for Foreign Affairs Simon Coveney said the European Union is trying to provide reassurance on Britain's exit deal but will not reopen the text of the agreement.
"This isn't just about Westminster," Mr Coveney said.
"This is a deal that has to get through a European parliament as well."
British Prime Minister Theresa May is seeking changes to her Brexit deal after parliament rejected it due to concerns among many MPs that the backstop, could see Britain trapped in the customs union long term.
"We can't reopen the Withdrawal Agreement for that to be renegotiated or changed, and so we are in the space of trying to provide reassurance and clarification for the British parliament to allow them to ratify this deal," Mr Coveney said.
He said there are some flexibilities Ireland can show after a deal has been done on Brexit, but Ireland cannot be asked to compromise the peace process in order to get a deal through.
Speaking on Sky News he said: "You can't ask Ireland to compromise on something as fundamental as a peace process and relationships linked to the Good Friday Agreement in order to get a deal through which is about placating a group within the Conservative Party who are insisting on moving the Prime Minister away from her own position.
"The idea that we would put a time limit to that backstop but not be able to answer the question 'What happens after that time limit runs out and what replaces the backstop?' - then it wouldn't be a backstop at all."
He added: "The Withdrawal Agreement is not up for renegotiation. The Withdrawal Agreement wording is not going to change.
"The way to do this is to change the wording of the future relationship declaration that can help to provide more clarity and reassurance to Westminster."
The Tánaiste said the backstop was a British government construct as much as it was an EU and Irish one.
He said: "This is about shared responsibility for Britain and Ireland as co-guarantors of a peace agreement in Northern Ireland to ensure that we don't go backwards, that we don't as an unintended consequence of Brexit see the re-emergence of a physical infrastructure between two jurisdictions, a border infrastructure that in the past has had awful memories."
Additional reporting PA, Reuters