Update 1.35pm: Sinn Féin President Gerry Adams has said a deal between the Tories and the DUP has to be opposed.
Today sees talks to restore power-sharing resume in Belfast. But the DUP leader is due to meet British Prime Minister, Theresa May, for talks at Downing Street tomorrow.
The two party leaders are in discussions to try and form a minority government at Westminster.
Adams said: “We don’t believe that any deal between the DUP here and the English Tories will be good for the people here. And any deal which undercuts in any way the process here, or the Good Friday or other agreements is one which has to be opposed.”
Democratic Unionist Ian Paisley confirmed that progress had already been made across the weekend.
“Talks are going on, Arlene Foster has made that very,very clear. Our key interest is stability in the United Kingdom and we want to make sure that we have that”
Update 12.30pm: The Northern Ireland Secretary appears to have ruled out an independent mediator to chair talks to restore powersharing amid criticism his impartiality has been compromised by the anticipated Democratic Unionist/Conservative parliamentary deal.
James Brokenshire 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, was the "right approach".
His comments come as DUP leader Arlene Foster warned Stormont rivals participating in the faltering negotiations the "time for unreasonable behaviour and unrealistic demands is over".
The talks were paused over the General Election campaign.
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 is starting in Belfast on Monday.
However, a major question mark now hangs over the talks as a result of developments at Westminster.
Political rivals of the DUP are adamant the 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 chair from outside the UK and Ireland to be appointed.
Mr Brokenshire said there was a need to differentiate between politics at Westminster and Stormont.
"It is important to distinguish what happens at Westminster and the votes that take place here, and devolution and the obligations and responsibilities that we hold fast to in relation to Northern Ireland," he said.
Devolution in the North is based on the template laid out in the 1998 Good Friday Agreement.
The historic accord commits the UK Government to demonstrate "rigorous impartiality" when dealing with competing political views in the region.
The Secretary of State said the government remained "four square" behind the Good Friday accord.
Asked on Radio Ulster about his views on bringing in an independent chair, he said: "I think the point is that we have a process already which involves, yes, the UK Government, but the Irish Government and also the head of the Northern Ireland Civil Service (Sir Malcolm McKibbin).
"That was something that was working to bring the parties together.
"I think that remains absolutely the right way to approach this and let's not forget we only have until the 29th June, so let's actually focus on the issues at hand rather than process, let's actually focus on getting people together for the best interests of Northern Ireland - that is what we are focused upon in supporting that work and supporting that effort because that is really how we will take Northern Ireland forward."
Earlier: Talks to restore powersharing in the North will resume later amid uncertainty over the impact of the anticipated Democratic Unionist/Conservative parliamentary deal.
The faltering negotiations were paused over the General Election campaign.
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 is starting in Belfast.
But a major question mark now hangs over the talks as a result of developments at Westminster.
Political rivals of the DUP are adamant the 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.
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.
Devolution in the North is based on the template laid out in the 1998 Good Friday Agreement. The historic accord commits the UK government to demonstrate "rigorous impartiality" when dealing with competing political views in the region.
In light of events at Westminster, Enda Kenny called Mrs May on Sunday to warn her that the Good Friday settlement has to be protected.
Sinn Fein, the SDLP and Alliance have all made clear they will not accept reappointed Northern Ireland Secretary James Brokenshire as a talks facilitator.
The dispute has prompted renewed calls for an independent mediator from outside the UK and Ireland to be appointed.
On Sunday night, Mr Brokenshire insisted the Government remained committed to the principles of the Good Friday Agreement and to governing in the interests of all the people of the region.
He also warned that the latest deadline for agreement - June 29 - was "final and immovable".
Mr Brokenshire made clear the reintroduction of direct rule from Westminster is on the cards if an agreement does not materialise by that date.
Irish foreign minister Charlie Flanagan, who will take part in the opening exchanges at Stormont on Monday, said: "It is now more important than ever that we have effective devolved government in Northern Ireland, especially with Brexit negotiations due to begin shortly."
He added: "The Irish Government remains fully committed to ensuring that the Good Friday Agreement and subsequent agreements are upheld and implemented in full."
The institutions collapsed after the late Martin McGuinness quit as deputy first minister in protest at the DUP's handling of the ill-fated Renewable Heat Incentive (RHI) - an eco-scheme that left Stormont facing a £490 million overspend.
Powersharing structures meant Mr McGuinness's move forcibly removed DUP leader Arlene Foster from her job as first minister and triggered March's snap election.
The Assembly election campaign exposed many more 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.