"But, I don't believe a general election is that path to do that, and I don't believe that a government led by (opposition leader Jeremy Corbyn) is the path to do that either". If this does not happen, the United Kingdom will be announced new parliamentary elections.
The prime minister named the parties in a statement in which she called on opposition politicians in Parliament to "put self-interest aside" and find a consensus on Britain's path out of the EU. "For two years she has not contacted, not approached us, not reached out".
The prime minister is expected to hold meetings with both Tory Brexiteers and the DUP - both of which rejected her withdrawal deal earlier this week - on Thursday.
Backbench Labour MPs ratcheted up the pressure on Mr Corbyn after Mrs May came through the no confidence vote unscathed. Had they switched allegiance, the government would have lost by one vote: 315 to 316.
British Prime Minister Theresa May has urged MPs to come together to get Britain out of the EU.
However, she has been criticised for her unwillingness to compromise or alter her red lines. But Corbyn's plan is to try to force the Prime Minister to rule out allowing a no deal Brexit, which experts and businesses have warned would cause grave damage to the United Kingdom economy, before committing to talks.
The BBC's political editor Laura Kuenssberg said it wasn't a straightforward judgement for the Labour party, as many members do not want Brexit to happen - meaning Mr Corbyn could quite easily be criticised for helping the process if he attends.
The Lib Dems, the SNP and Plaid Cymru all spoke with Theresa May on Wednesday.
May's Brexit deal suffered a crushing defeat in parliament on Tuesday, triggering political chaos that could lead to a disorderly exit from the European Union, a reversal of the 2016 decision to leave or a compromise deal of some sort.
After defeating the no-confidence motion, May said she would hold talks "in a constructive spirit" with leaders of opposition parties and other lawmakers in a bid to find a way forward for Britain's European Union exit. The "door remains open" for the Labour leader to join the talks, May said. The preferred choice of the party is a second referendum.
Faced with the deadlock, lawmakers from all parties are trying to wrest control of the Brexit process so that Parliament can direct planning for Britain's departure. She has been reluctant to do so up until now because pro-Brexit Conservative MPs want to see this hardest of Brexits remain a viable option.
May also reiterated a promise to return to the Commons on Monday to give MPs another vote on her plans.
"The confidence and supply arrangement (to support May) of course is built upon delivering Brexit on the basis of our shared priorities," said Nigel Dodds, deputy leader of the Democratic Unionist Party.
Labour's Corbyn said he would not meet with May until she ruled out a no-deal Brexit.
"The only feasible way to do this is by asking the people whether they still want to leave the European Union. politicians must not waste any more time on fantasies".
"Either he backs Brexit or he backs the people", Liberal Democrat leader Sir Vince Cable said.