Since the March 2017 legislative assembly elections, Irish nationalists of the Sinn Fein party and pro-British unionists under the DUP have been unable to find common ground on divisive issues such as the introduction of an Irish language act and legacy issues inherited from decades of violence popularly known as "the Troubles". "There was talk about a free-standing Irish Language Act...but we won't be agreeing to an Irish Language Act...we've always said that was a step too far".
"So we will be making it very, very clear to anybody who will listen that this can not be direct rule with the DUP having the whip hand, but it looks to me, today, this is what these negotiations are about to deliver - that has to be resisted at all costs".
Mrs Foster added: "Restoring a sustainable and fully functioning devolved government will remain our goal but we will not accept a one-sided deal".
But Mrs Foster said while the leaders were welcome, their presence proved a "bit of a distraction" as it interrupted negotiations.
"Sinn Fein's insistence on a stand alone Irish Language Act means that we have reached an impasse", Foster said. "I believe the basis for an accommodation (between the parties) still exists".
"There won't be a stand-alone Irish Language Act - we have always made that very clear, people aren't going to be forced to learn Irish, there isn't going to be Irish compulsory in schools, there's not going to be bilingual signs or quotas in the civil service", she said.
"Print it, publish it online - do it whatever way they want, but it is vitally important that the people of Northern Ireland know what accommodation they did reach", he said. I respect the Irish language and those who speak it but in a shared society this can not be a one-way street.
She said: "In our view, there is no current prospect of these discussions leading to an Executive being formed".
Sinn Féin's Northern Ireland leader Michelle O'Neill said that the party had stretched itself, and blamed the DUP for collapsing a process aimed at rebuilding coalition government at Stormont after a 13-month suspension. The DUP failed to close the deal.
The previous local administration collapsed in January 2017 with the resignation of Sinn Fein Deputy First Minister Martin McGuinness over a botched energy saving deal.
As talks broke up on Monday night Mrs May urged the parties to make "one final push" to strike a deal to salvage powersharing.
Bradley said in the continued absence of an executive "other challenging decisions will have to be taken by the United Kingdom government". Power-sharing and working together are the only way forward for Northern Ireland.
The issue has proven to be the main sticking point in over a year of negotiations but in the past week it had been thought that progress has been made.
"We will need to reflect in the coming days on how best to do that".