Politicians gathered at Stormont yesterday to begin a fresh round of negotiations in a bid to break the deadlock.
The new secretary of state, Karen Bradley was also present, along with Irish deputy prime minister Simon Coveney.
Taoiseach Leo Varadkar has also said he is ready to get involved in talks if he thought it could help.
But TUV leader Jim Allister said the Irish Government should have no role in issues relating to the internal affairs of NI, and questioned why the DUP and UUP are engaging with Mr Coveney.
Mr Allister also claimed that five Dublin officials have been given passes which grant them “unfettered access” to parliament buildings during the talks.
“This under the oversight of the Assembly Commission on which the DUP and UUP quietly sit,” the North Antrim MLA added.
Highlighting that former Ulster Unionist leader David Trimble had refused to engage with the Irish government when strand one issues were discussed during the Belfast Agreement, Mr Allister asked: “Where are the unionist objections to Simon Coveney’s role?
“This is a seminal point of constitutional importance yet unionists accept the involvement of a foreign government in our internal affairs without a whimper.”
In response to Mr Allister’s remarks, the DUP last night accused him of “picking holes with fellow unionists”.
A party spokesperson told the News Letter it will be discussing matters of “mutual relevance” with the Irish Government, adding that Dublin “recognises the limitations and parameters of their involvement within any talks”.
Meanwhile, the UUP said it “was not discussing the internal affairs of NI”.