"We all have an interest.in keeping them as close as possible to the European Union, because Britain is an important country, vital to the EU in the security and foreign policy realm, and naturally also a part of the European market", he said.
If Britain changes track and decides to remain a member of the European Union it could lose perks such as budget rebates and opt-outs, according to the European Parliament's Brexit coordinator.
The London fire, which claimed at least 17 lives, forced the cancellation of the City of London's Mansion House dinner, where May's finance minister, Philip Hammond, had the chance to revive calls for a more business-friendly exit from the EU.
As Britain entered a sixth day of political turmoil, Mrs May's team continued talks with Northern Ireland's Democratic Unionist Party (DUP) to secure their support after the Prime Minister failed to win a majority in last Thursday's election.
Conservatives and the DUP are committed to strengthening British unity, delivering Brexit, combating terrorism and delivering prosperity but "at the moment there isn't a deal", the source said. "I agree", Mr Verhofstadt said.
But speaking in Strasbourg, Guy Verhofstadt, the former Belgian Prime Minister, who is now responsible coordinating the European Union parliament's Brexit stance, suggested there would be a price to pay should Britain wish to remain in the bloc.
Speaking to reporters in Paris late Tuesday, Mrs May sought to dispel those fears, saying "we as Government remain absolutely steadfast" in its commitments to the Northern Irish peace process.
The SNP's James Dornan asked the First Minister if she shares his concern about the message a deal between the Conservatives and the DUP, who have used their veto to block legalising same-sex marriage in Northern Ireland five times, sends to the LGBTI community. You folk here made enough mess of our own elections, make enough mess of your own governments, make enough mess of your own affairs.
Trump touts apprenticeships to strengthen young United States workers
But his own proposed budget would cut other job training programs that advocates say are necessary for this one to thrive. He said they were joined by governors from around the country who had just spoken about apprenticeship programs.
The government meanwhile said the state opening of the British parliament - when May's government presents its legislation programme - will take place on June 21, two days later than planned.
"The door of course is still open as long as Brexit negotiations have not been concluded", he said.
The Conservative source said: "We're confident of getting an agreement, we're confident that the Queen's speech will be passed".
"I cannot see for the life of me how you can be a neutral facilitator in bringing the parties together, at a very risky time for Northern Ireland politics to get self-government and the legislative assembly back up and running, when your prime ministerial life and your government's life depends on one of the most influential parties - the biggest party - in Northern Ireland", Lord Hain said.
Davis plans to go to Brussels on Monday to start the negotiations, which will reshape not only Britain's role in the world, but also that of a bloc praised for ensuring peace after World War Two.
May will host Arlene Foster in Downing Street to discuss terms of the DUP's backing for her minority government, reports the BBC.
But with the two-year countdown to Brexit already under way after Article 50 was triggered in March, he said: "We are impatiently waiting for the negotiating position of the United Kingdom gov".
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