The DUP's Jeffrey Donaldson claims Simon Coveney has "crossed the line" during negotiations
Stormont talks could be suspended today if there is not a breakthrough.
The fourth deadline to form a Government in the North passed yesterday without a deal.
Sinn Féin and the DUP are believed to be at odds over issues such as the Irish Language Act.
The UK's Northern Secretary James Brokenshire indicated in the House of Commons yesterday that that he believes "a deal remains achievable".
However, he added: "If no agreement is reached, legislation in Westminster may then be required to give authority for the expenditure of Northern Ireland departments through an Appropriations Bill."
The new Foreign Affairs Minister Simon Coveney has been among those trying to break the deadlock - but the DUP's chief negotiator Jeffrey Donaldson suggests he is not helping.
Speaking on Newstalk Breakfast, Mr Donaldson explained: "There's a clear designation as to what the Irish Government can and should be involved in - and I'm afraid Minister Coveney has crossed the line on that on occasion.
"I hope that is just because he hasn't been involved before, and not a sign that there is a marked shift in the approach of the Irish Government."
He added: "If that were be the case, and the Irish Government were trying to muscle in on issues that are internal to Northern Ireland and create the impression of a pan-nationalist front [...] that would be counterproductive."
He said that he does not see an agreement reached this week unless there is a 'significant change' in the next few days - but stressed that "it's always possible".