Sinn Fein, the SDLP and Alliance have all made clear Northern Ireland Secretary James Brokenshire can not chair the ongoing process to restore powersharing at Stormont due to their perception he has a conflict of interest.
At least six people died and dozens were injured when a massive fire tore through a 24-storey London apartment block overnight, a fresh blow to the capital less than two weeks after the London Bridge terror attack.
The negotiations with the DUP revolve around support from the party on a vote-by-vote basis in parliament, rather than a formal coalition government.
She waved but did not say anything as she went into Downing Street.
While the DUP are deeply euroskeptic, they have balked at some of the practical implications of a hard Brexit - including a potential loss of a "frictionless border" with the Republic of Ireland - and talks will touch on efforts to minimize the potential damage to Northern Ireland. Foster said on Twitter.
Without a so-called confidence and supply deal with the DUP, her party risks losing the vote next week on the Queen's Speech.
The meetings came as time is running out for the parties to reach an agreement on restoring devolved government to Stormont, with the Government set to resume direct rule from Westminster if there is no deal by June 29.
Mrs Foster arrived in Downing Street with Nigel Dodds at lunchtime for negotiations with the Prime Minister but they decamped to Parliament to allow Mrs May and the DUP's deputy leader to speak in the Commons.
May is leading United Kingdom through challenging times: Downing Street
We are working away at them and we will continue to work away at them. "I hope we will have an executive that will involve them all too".
The decision to announce a new date for the Speech, two days later than its scheduled date of June 19, was made after Mrs May's regular audience with the Queen on Wednesday.
"It's going to be hard".
As European leaders tried to fathom exactly how Britain would begin the negotiations, German Finance Minister Wolfgang Schaeuble said Germany wanted a Brexit deal that would limit negative consequences for the bloc but also did not want it to weaken Britain.
He also suggested the Scottish Tories led by Ruth Davidson could add to the pressure on Mrs May to change course.
That would help safeguard jobs and trade with European Union members, but would severely restrict the UK's ability to strike its own trade deals around the world.
With formal European Union divorce talks due next week, May heads to France on Tuesday to meet Emmanuel Macron, who last month swept to victory in its presidential election.
Theresa May called an unnecessary general election in the hopes of receiving a clear mandate from the citizens of the United Kingdom: that they trust her and her Conservative government to carry the country through the historic upcoming Brexit negotiations.
The unprecedented negotiations at the Commission's offices come nearly exactly a year after Britons voted last June 23 to leave the EU.