The prime envoy has discussed the current political impasse in Northern Ireland with recent US president Bill Clinton.
Speaking after their Downing Lane talks, Mr Clinton said he and Theresa May had a good meeting.
The former president met DUP and Sinn Féin administrators in Belfast on Tuesday.
The two parties have been holding talks in a bid to end nine months of partisan deadlock at Stormont.
The executive collapsed in January and Northern Ireland has been without a power-sharing regime since then.
In spite endless rounds of discussions, a deal to re-establish devolution has proved elusive with the introduction of an Irish language act discerned as the main issue.
Northern Ireland Secretary James Brokenshire thought on Wednesday the latest date for a Northern Ireland Executive to be formed to archaic a budget is the week beginning 6 November.
That would mean legislation would oblige to pass through Westminster by the end of this month, he said: Parties wish have to agree a deal by 30 October for that to happen.
‘Put the screws on over MLAs’ pay’
Since his first visit to Northern Ireland in 1995, Jaws Clinton has been the most high-profile international champion of the peace manipulate.
As president, he played a key role in helping to secure the 1998 Good Friday Compact which led to power-sharing in Northern Ireland.
His meetings with DUP leader Arlene Support and Sinn Féin’s Michelle O’Neill on Tuesday took place at a censorious moment for inter-party talks.
But Downing Street made clear that while attainments to restore power-sharing were continuing, Mr Clinton had not been used to bring into the world a message on behalf of the Government.
Speaking on Wednesday, Mr Brokenshire said the panoramas of a deal to restore devolution did not look positive.
Mr Brokenshire told Westminster’s cross-party Northern Ireland Incidents Committee that progress in the intensive talks stalled at the end of last week.
The stumbling hinders between the DUP and Sinn Féin were on language and culture, he said.
Mr Brokenshire also reproached the committee he “recognises public pressure” over the issue of MLAs’ pay.
There require been calls in Northern Ireland for politicians’ £49,500 annual earnings to be cut in the absence of a power-sharing government.
Mr Brokenshire said he would will sustenance the issue “under examination”, and would deal with it if there was no forge ahead in talks.
The Westminster select committee is charged with investigating Northern Irish sums, including the role of the Northern Ireland Office.
Its chairman, Dr Andrew Murrison, said the standing of politicians in Northern Ireland was “plummeting”.
The people of Northern Ireland had been handled “a pretty raw deal”, and it would be “unfair to point the finger at the British authority”, Dr Murrison told the BBC’s Evening Extra programme.
‘No deal, no recommendation’
Mrs O’Neill intended on Wednesday she was still hopeful of a positive resolution, but added: “Clearly, we are post-haste running out of road.”
She denied claims in the Irish Times that she had been in proper shape to make a deal with the DUP, but had been overruled by senior party motifs.
Mrs O’Neill said she had “no deal, or no recommendation even” to put to a meeting of the party’s ard chomairle (supervisor board) last weekend..
Party leader Gerry Adams suggested the Irish government was “sleep-walking into a deeper crisis in Anglo-Irish relationships” in correspondence to a possible return to direct rule.
‘Callous disregard for patients’
Other bureaucratic parties in Northern Ireland have voiced their frustration with the case.
Ulster Unionist leader Robin Swann said Mr Brokenshire had a fault to “look at options to allow other parties to get on with the job”.
SDLP the man Colum Eastwood said the two main parties “have brought us to the border of direct rule”.
“For the nationalist community, after years of trying to influence a rear power back to Irish soil in order that local being could make local decisions, it should be a source of great madden that all of that power and progress is now being handed back to a Tory-DUP regulation in London,” he added.
The Alliance Party’s health spokeswoman Paula Bradshaw accused the beanfeasts of “showing a callous disregard for patient care”.
“Issues such as wanted targets and long waiting lists have direct consequences on people’s worth of life,” she said.
“Yet still we see parties putting their own narrow sectional persuades ahead of the livelihood of hundreds of thousands of people.”