Relations between the taoiseach and secretary of state appeared strained on Monday in the aftermath of the launch of a fresh tranche of peace-building funds.
Chris Heaton-Harris accused Leo Varadkar making "unhelpful comments" that were undermining efforts to restore the institutions.
For his part, the Fine Gael leader defended last week's restatement of his belief that there will be a united Ireland in his lifetime, while he also urged the British government to "pause" its controversial legislation for dealing with the past.
The diplomatic spat unfolded in south Belfast at the launch of a €1.14 billion (£978 million) fund targeting Northern Ireland and the Republic's border counties.
The PEACEPLUS funding programme replaces the EU's PEACE programme and is designed to support peace and prosperity across a range of sectors.
The scheme is a partnership between the British and Irish governments, the EU and the Northern Ireland Executive.
As well as the taoiseach and secretary of state, the event was attended by vice-president of the European Commission Maros Sefcovic, Irish Public Expenditure Minister Paschal Donohoe and the regional head of the civil service Jayne Brady.
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Speaking at the event, Mr Sefcovic said the funding was a demonstration that the contributors were "putting their money where their mouth is".
"Here in Northern Ireland, we have seen how peace, when it is not a given, becomes an overwhelming desire, a primary necessity – and how much we can achieve when we put our minds and hearts to it," he said.
Mr Heaton-Harris said the British government, which is providing more than £730 million of the funding, was "committed to helping Northern Ireland to reach its full potential as a prosperous and stable part of the United Kingdom".
Taoiseach Leo Varadkar said the scheme was a reminder of what was possible, despite the lack of a functioning Stormont executive.
But in the press conferences by the taoiseach and secretary of state that followed, tensions appeared to emerge.
Mr Varadkar said during his meeting with the secretary of state he had urged the British government to "pause" its controversial legacy bill.
He said the Irish government had yet to make a decision on whether to mount a legal challenge against the bill.
"That is a big decision, it is not a small thing to do to take a neighbouring state to court," he said.
"Before we make that decision we are going to need to seek legal advice from our own attorney general and we shall do that in the next couple of weeks."
The Fine Gael leader also told Mr Heaton-Harris that a point is coming when "alternative arrangements" will need to be discussed to address the absence of power-sharing.
"I did say to the secretary of state that there is going to come a point where we can't keep waiting and we have to start talking about alternative arrangements within the confines of the Good Friday Agreement," he said.
The taoiseach defended his remarks about Irish unity.
"Every time I say it, it is not the right time – so I would often ask the question, when is the right time?" he said
"I stated very clearly that I believe the success of a united Ireland would be judged on how we treat our minorities – that is how you judge the success of states."
Mr Heaton-Harris insisted progress was being made in the effort to restore Stormont and that it was his priority.
"There are always plenty of people who are willing to point out when obstacles are put in the way," he said.
"The taoiseach's got a lot of domestic politics on his plate, but occasionally unhelpful comments down in Dublin do resonate up here amongst the unionist community, and I need the clearest picture possible to get the executive up and running."
The secretary of state also criticised remarks by the taoiseach for a "plan B" if the current impasse continued.
"I'm keen to make sure that we come to a conclusion and the executive is up and running in the shortest period of time," he said.
"And as I just said, talk of plan B is unhelpful."