The British government and the main opposition were to hold further crisis talks on Thursday after MPs voted in favour of a Brexit delay that would avoid Britain crashing out of the EU on April 12.
With options running out, May switched course and invited Labour leader Jeremy Corbyn for talks on Wednesday in a bid to forge a compromise that avoids a chaotic "no-deal" departure from the European Union in eight days' time.
Negotiating teams for both sides were to meet again on Thursday for a full day of urgent discussions.
May's divorce deal with the other 27 EU nations has been rejected three times by parliament and patience is wearing thin in Brussels as the deadline to end Britain's 46-year membership nears with no agreement in sight.
The premier said Tuesday she would seek another "short" Brexit extension at an EU leaders' summit in Brussels on April 10.
In a rushed parliamentary bid to avoid Britain leaving the EU without a divorce deal next Friday, MPs voted by the narrowest of margins late Wednesday in favour of draft legislation that would force the government to seek to delay Brexit beyond April 12.
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The vote passed by just one -- 313 votes in favour and 312 against -- in the lower House of Commons and the bill will now pass to the upper House of Lords for final approval on Thursday, much to the government's annoyance.
"We are disappointed that MPs have chosen to back this bill," a government spokesman said.
"The prime minister has already set out a clear process through which we can leave the European Union with a deal and we have already committed to seeking a further extension.
"If passed, this bill would place a severe constraint on the government's ability to negotiate an extension and reflect this new date in UK statute books before April 12."