The Prime Minister has warned Northern Ireland's rowing politicians that time is running short to salvage the powersharing institutions.
Theresa May said she believed a deal could be reached to restore a devolved coalition administration in Belfast if "there is good will on all sides".
Her comments came after she held separate meetings with leadership figures in all five main parties at Downing Street.
While her statement did not touch on her likely parliamentary deal with the Democratic Unionists, that issue was high on the agenda during the private meetings.
A number of the parties raised serious concerns about the potential impact any arrangement might have on the ongoing process to re-establish devolved government at Stormont.
Sinn Fein, the SDLP and Alliance Party have all questioned the ability of the Government to fulfil its obligation - under the Good Friday Agreement - to act with impartiality in Northern Ireland in light of its link-up with the DUP.
Mrs May said: "Speaking with the parties today, it was clear that real progress was made in the last round of discussions and agreement can be reached if there is good will on all sides.
"But time is running short and the parties must come together by the 29 June for the return of a strong voice at Stormont and for a brighter future for everyone in Northern Ireland.
"My Government remains absolutely committed to doing everything we can to help take this process to a successful conclusion, remaining steadfast to our commitments in the Belfast Agreement and its successors.
"The Northern Ireland Secretary will continue to engage with the parties before this crucial deadline and if no resolution is reached then we will need to consider what steps we need to take, to ensure Northern Ireland has the political stability it needs."
Northern Ireland has been without a powersharing Executive since March and without a First and Deputy First Minister since January.
The institutions collapsed amid a bitter row between the DUP and Sinn Fein about a botched green energy scheme.
The Government has warned that direct rule from London could be reimposed if the local parties fail to reach an agreement before the June 29 deadline.
The Prime Minister also discussed the current impasse at Stormont in a telephone conversation with newly elected Irish Taoiseach Leo Varadkar on Thursday.
Emerging from Downing Street, Sinn Fein president Gerry Adams accused Mrs May of playing "fast and loose" with the Good Friday Agreement.
He also claimed she was turning a "blind eye to the disruptive actions" of the DUP at Stormont.
"Both the Government and the DUP have refused to implement key agreements on language and equality rights and dealing with the legacy of the past," he claimed.
Mr Adams added: "We warned Mrs May that the pact between the Tories and the DUP has the potential to undermine past agreements and the re-establishment of the Executive.
"Any deal that undermines the Good Friday Agreement will be opposed by Sinn Fein and we would hope the Irish Government.
"If the institutions are to be put in place they need to be sustainable, viable and properly resourced."
DUP deputy leader Nigel Dodds said he emphasised to Mrs May that his party stood ready to form a new powersharing executive "without any preconditions or red lines".
"We don't think there is a need to further delay a process that should be put in place to address the needs of the people of Northern Ireland," he said.
"These are the priority issues for us. We will engage intensely to make that happen.
"We are certainly up for the task of getting devolved government back up and running in Northern Ireland."
Sinn Fein, the SDLP and Alliance have demanded that Northern Ireland Secretary James Brokenshire step aside from chairing any part of the talks.
The head of the Northern Ireland Civil Service, Sir Malcolm McKibbin, has already taken on responsibility for moderating many of the exchanges, with Sinn Fein and the SDLP having already questioned the impartiality of Mr Brokenshire earlier in the process.
But Ulster Unionist leader Robin Swann said talk of replacing Mr Brokenshire or appointing an independent chair from outside the UK and Ireland was a "sideshow".
"We have two weeks from today to get the Northern Ireland executive up and functioning again and to try to bring in a new chair is actually a waste of time and a distraction," he said.
"The Ulster Unionist Party is prepared, as we have always been prepared, to get the executive up and functioning again."
SDLP leader Colum Eastwood said the Prime Minister had not convinced him the "DUP tail is not wagging the Tory dog".
"We were very clear that it can't be a deal that gives the DUP power over the Tory Party," he said.
"It can't be a deal that affects and infects the talks process."
Alliance leader Naomi Long struck a more optimistic note as she left Downing Street.
"We remain optimistic that a deal (on powersharing) can be done if others have the will to do so," she said.