Labour leader Jeremy Corbyn said he would not talk to her about changes to the Brexit deal unless she takes the no-deal possibility off the table.
May said outside No 10 Downing St: "I am inviting MPs from all parties to come together... This is now the time to put self-interest aside ... I am disappointed that the leader of the Labour Party has so far decided not to take part but my door is open."
Legislators ripped up May's Brexit blueprint yesterday by rejecting the divorce agreement she negotiated with the EU over the last two years. That it would lose was widely expected, but the scale of the rout — 432 votes to 202, the biggest defeat government defeat in British parliamentary history — was devastating for May's leadership and her Brexit deal.
Corbyn responded with the no-confidence motion, and urged the Government to "do the right thing and resign".
May, who leads a fractious government, a divided Parliament and a gridlocked Brexit process, said she was staying put.
May said an election "would deepen division when we need unity, it would bring chaos when we need certainty, and it would bring delay when we need to move forward."
The Government survived today's vote with support from May's Conservative Party and its Northern Irish ally, the Democratic Unionist Party. May would have lost by one vote if the DUP had voted with the opposition.
Many pro-Brexit Conservatives who voted against May's deal, backed her in the no-confidence vote to avoid an election that could bring a left-wing Labour government to power.
Had the Government lost, Britain would have faced a snap election within weeks, just before the country is due to leave the European Union on March 29.
Political analyst Anand Menon, from the research group UK in a Changing Europe, said May had a remarkable ability to soldier on.
"The thing about Theresa May is that nothing seems to faze her," he said. "She just keeps on going."
May's determination — or, as her foes see it, her inflexibility — might not be an asset in a situation calling for a change of course. The Prime Minister has until Tuesday NZT to come up with a new Brexit plan.
May promised to speak to MPs from across the political spectrum. But she also said any new Brexit plan must "deliver on the referendum result," which May has long interpreted to mean ending the free movement of workers to Britain from the EU and leaving the EU's single market and customs union.
Many MPs think a softer departure that retained single market or customs union membership is the only plan capable of winning a majority in Parliament.
They fear the alternative is an abrupt "no-deal" withdrawal from the bloc, which businesses and economists fear would cause turmoil.
Labour MP Ben Bradshaw accused May of being "in a total state of denial" about how radically her Brexit plan needed to change.
Green party legislator Caroline Lucas said May's intransigence had led to the current crisis.
"This is a national calamity of the prime minister's own making," Lucas said. "Today has to be the day when we start to change the conversation about Brexit."
Faced with the deadlock, MPs from all parties are trying to wrest control of the Brexit process so that Parliament can direct planning for Britain's departure.
But with no clear majority in Parliament for any single alternative, there's a growing chance that Britain may seek to postpone its departure date while politicians work on a new plan — or even hand the decision back to voters in a new referendum on Britain's EU membership.
European leaders are now preparing for the worst, although German Chancellor Angela Merkel said there was still time for further talks. She told reporters in Berlin that "we are now waiting to see what the British prime minister proposes."
But her measured remarks contrasted with the blunt message from French President Emmanuel Macron, who told Britons to "figure it out yourselves". He said Britain needed to get realistic about what was possible.
"Good luck to the representatives of the nation who have to implement something that doesn't exist," Macron said.
EU Brexit negotiator Michel Barnier said the bloc was stepping up preparations for a disorderly no-deal Brexit after Parliament's actions left Europe "fearing more than ever that there is a risk" of a cliff-edge departure.
Economists warn that an abrupt break with the EU could batter the British economy and bring chaos at borders, ports and airports. Business groups have expressed alarm at the prospect of a no-deal exit.
- AP
