DUP leader Arlene Foster has told Sinn Féin leaders if they are concerned about her party's enhanced influence at Westminster they should move to restore devolution at Stormont.
Mrs Foster delivered the blunt message to the republican party as she rejected its claim the anticipated DUP/Conservative deal at Westminster would undermine the political process in the North.
She warned that a consequence of failing to re-establish a powersharing executive would be the return of direct rule, with decisions on devolved issues being taken by the British government.
"If others decide that they are not coming back into the devolved administration here in Northern Ireland then those issues will have to be dealt with at Westminster," she said.
"It is really for Sinn Féin to decide where they want those powers to lie."
Her remarks came after Sinn Féin and other Stormont parties insisted Northern Ireland Secretary James Brokenshire could not chair the efforts to restore powersharing.
They are adamant the UK Government can no longer cast itself as a neutral facilitator in the process, given Theresa May's intent to form a minority government with the help of a confidence-and-supply deal with the unionist party.
The dispute has prompted renewed calls for a chairman from outside the UK and Ireland to be appointed.
Sinn Féin President Gerry Adams (pictured) said: "Our resolve is to see these institutions put in place on the basis they were founded upon as quickly as possible. That could be done this time tomorrow morning or dinner time today. They are all rights issues subject to previous agreements.
"We made clear at the beginning of these talks that James Brokenshire is not an acceptable chair."
Earlier, Mr Brokenshire appeared to rule out an independent mediator to chair the Stormont talks.
He said the current process - which involves the UK and Irish governments chairing elements of the negotiations and the head of the Northern Ireland Civil Service moderating other discussions - is the "right approach".
SDLP leader Colum Eastwood warned that the future of the North could not be left "in the hands of a Tory-DUP government."
"If James Brokenshire thinks for one second he can be an independent chair of these talks he is absolutely wrong," he said.
"I have said it for the last six months, this talks process needs an independent chairman to get things done."
With the North having been without a powersharing executive since March and without a first and deputy first minister since January, a new three-week process to salvage devolution began in Belfast on Monday.
A major question mark hangs over the talks as a result of developments at Westminster.
A number of deadlines to reach an agreement have already fallen by the wayside since March's snap Assembly poll, which was triggered by the implosion of the last DUP/Sinn Féin-led administration over a dispute about a botched green energy scheme.
The Assembly election campaign exposed many divisions between the two main parties on issues such as legislative protections for Irish language speakers and how to deal with the legacy of the Troubles.
Devolution in the North is based on the template laid out in the 1998 Good Friday Agreement.
The accord commits the Irish and UK governments to demonstrate "rigorous impartiality" when dealing with competing political views in the region.
DUP deputy leader Nigel Dodds asked would Sinn Féin rule itself out of any future coalition government in the Irish Republic?
"I think the people of the Irish Republic would be very, very interested, as would other members of other political parties, to know before they fight the next general election in the Irish Republic whether or not Sinn Féin are going to rule themselves out of government on the basis that is a breach of the Good Friday Agreement? Because if that's what they say about us, then it applies to them equally," he said.
Mr Brokenshire, who said the British government remained "four square" behind the Good Friday deal, has warned the latest deadline for agreement - June 29 - is "final and immovable".
He made clear the reintroduction of direct rule from Westminster is on the cards if an agreement does not materialise by that date.
Irish foreign affairs minister Charlie Flanagan said it was important that all of the parties and both governments ensure the deadline is met for restoration.
He added: "While the landscape has dramatically changed over the weekend the issues are exactly the same. We want to ensure that every opportunity is given to the parties here to have the powersharing institutions restored."