"Discussions are going well with the government and we hope to bring this work to a successful conclusion soon", said the DUP's Arlene Foster after the meeting.
Sir Keir said the loss of Mrs May's overall majority in the June 8 General Election meant Parliament could no longer be "marginalised" in the Brexit process and "appropriate steps" must be taken to prepare for a Labour administration to take over negotiations at any stage if Mrs May's Government falls.
The talks revolve around support from the DUP on a vote-by-vote basis in parliament, rather than a formal coalition government.
The spokesman said the UK's "first aim" was to move ahead on securing the rights of European Union citizens in the United Kingdom and UK citizens living in the EU.
"The danger is that however much any government tries they will not be seen to be impartial if they are locked into a parliamentary deal", former Conservative prime minister John Major told BBC radio.
She is also trying to contain outrage at home over a London tower block fire which left at least 30 people dead.
The DUP is believed to be more favourable to a "soft Brexit" that would keep Northern Ireland's border with the Republic of Ireland free-flowing.
Brexit negotiations were scheduled to start in earnest next Monday. "It may not be on the Monday because we've also got the Queen's Speech that week and I will have to speak in that and so on".
Robert Mueller is investigating Jared Kushner and his finances
But soon after the abrupt termination, Trump told NBC News that he had been going to fire Comey regardless of any recommendations. Dianne Feinstein, the panel's ranking Democrat, has called for an investigation into any possible obstruction by the President.
Prime Minister Theresa May wants to negotiate the divorce and the future trading relationship with the European Union before Britain leaves in March 2019, followed by what she calls a phased implementation process to give business time to prepare for the impact of Brexit.
The European Commission said the one-day meeting between its chief negotiator Michel Barnier and Brexit Secretary David Davis will take place "as part of the sequenced approach to the talks" set out by the EU, which require progress to be made on withdrawal arrangements before any talks on trade can begin.
May's finance minister, Philip Hammond, said on Friday that Britain should prioritize protecting jobs and economic growth.
A spokesman for his Department for Exiting the European Union said Britain had been "crystal clear" about its approach.
"My clear view, and I believe the view of the majority of people in Britain, is that we should prioritize protecting jobs, protecting economic growth, protecting prosperity as we enter those negotiations", Hammond told reporters before a meeting of the 28 European Union finance ministers in Luxembourg.
"We believe that the withdrawal process can not be concluded without the future relationship also being taken into account", the spokesman said.
But after a generation of discord over Europe inside her party, May's future could depend on her ability to please both the eurosceptic and pro-European factions in her party.
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