He says he won't talk to her unless she rules out a no-deal Brexit from their discussions. While the prospect of a no-deal Brexit is of course concerning to them, the remaining European Union member states are prepared to weather the storm of a no-deal if they must.
On Thursday, in order to break the impasse and shape a Brexit plan that might pass a spectacularly divided Parliament, May held meetings with leaders of opposition and independent parties at 10 Downing Street.
Prime Minister Edouard Philippe told reporters on Thursday that there were "strong fears" Britain would leave without a deal on March 29.
A no-confidence motion tabled by Labour was defeated by 325 votes to 306 - with the victory margin of 19 significantly larger than Mrs May's effective majority of 13.
"Now MPs have made clear what they don't want, we must all work constructively together to set out what parliament does want", May said in a televised address to the nation on Wednesday evening, after winning a no-confidence vote triggered by the opposition Labour party.
France this morning pushed the button on a €50m (£44.24m) contingency plan to deal with the fallout from a potential no-deal Brexit.
Friends of Lucas said that May pushed back on the idea of a second referendum, arguing it would "look bad for parliament if it could not fulfil this instruction of the British people".
"So there are two ways to avoid no deal: either to vote for a deal, in particular a withdrawal agreement, that has been agreed with the European Union, or to revoke Article 50 and overturn the referendum result", she said.
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Iran, meanwhile, has continued to develop more sophisticated ballistic missiles, increasing their numbers and their capabilities. For years, USA missile defenses have focused exclusively on combating threats from rogue nations such as North Korea and Iran.
Although Wednesday's no-confidence vote left May in office, she saw more of her power ebb away as she battled to keep Brexit on track after lawmakers demolished her European Union divorce deal. The country feels genuinely sorry for the prime minister.
And what's more, Mr Corbyn has told his MPs not to talk to her ministers either.
May must "do the right thing and resign", said Corbyn.
But Mr Corbyn immediately rejected the invitation, saying he would not participate unless Mrs May ruled out a no-deal departure from the bloc in March.
Another backbench Labour critic, the east London MP Mike Gapes, criticised the party leader's attitude to talks, tweeting: "Apparently Corbyn is prepared to hold talks with Hamas, Hezbollah, Assad and Iran without preconditions".
Labour's Shadow Brexit Secretary Sir Keir Starmer also spoke on Tuesday to endorse the policy of "going back to the people".
He confirmed that Labour will table amendments to Monday's motion, putting forward its preferred solution of a customs union with a voice for the United Kingdom in future EU trade deals, a close single market relationship and protections for rights.
"If anybody believes that you can just go ahead without some sort of an agreement here, I think that that is reckless", said John Bason, finance chief of Associated British Foods, a food and retail group with annual sales of over US$20 billion (S$27.1 billion). "A no-deal Brexit would be a disaster for British science and innovation and I urge our elected representatives to put the interests of the country first and get a new plan to prevent this catastrophic outcome".