Theresa May has called on MPs to “put self-interest aside” and “work constructively together” to find a way forward for Brexit.
Earlier, the prime minister won a vote of no confidence by 325 to 306, as rebel Tory MPs and the DUP backed her to stay in No 10.
But just 24 hours before, both groups ensured her Brexit plan was voted down.
On Wednesday night the PM met the SNP, Lib Dem and Plaid Cymru leaders but not Labour leader Jeremy Corbyn.
She said: “I am disappointed that the leader of the Labour Party has not so far chosen to take part, but our door remains open.”
Mr Corbyn has said that before any “positive discussions” can take place, the prime minister should rule out a no-deal Brexit.
The BBC’s political editor, Laura Kuenssberg, said Labour had been clear that unless Mrs May makes a statement saying the UK will only leave through a managed process, Mr Corbyn is not going anywhere near the talks.
But she 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.
MPs voted against Mrs May’s plans for Brexit on Tuesday night by an historic margin when it was rejected by 230 votes – the largest defeat for a sitting government in history.
‘Duty to deliver Brexit’
Speaking outside Number 10, Mrs May said: “I understand that to people getting on with their lives away from Westminster, the events of the past 24 hours will have been unsettling.
“Overwhelmingly the British people want us to get on with delivering Brexit and also address the other important issues they care about.
“I believe it is my duty to deliver on the British people’s instruction to leave the European Union and I intend to do so.”
The prime minister said the meetings she had held so far had been “constructive” and that she – along with other senior government representatives – would be meeting with other MPs in the coming days to get the “widest possible views across parliament” on Brexit.
Labour’s deputy leader, Tom Watson, earlier told BBC News that it was not “unreasonable” for Mr Corbyn to say: “Are you serious?”
He added: “We’re very amenable to talks, but I think the prime minister needs to show us that she’s actually serious about that.
“Is she actually going to concede on some of these red lines? Are they going to be meaningful to us?”
The Westminster leader of the SNP, Ian Blackford, wrote to the PM following his meeting, calling for a “clear gesture of good faith” from her.
He said that the extension of Article 50 – the mechanism that allows the UK to leave the EU – the ruling out of a no-deal Brexit and the option of a second EU referendum would have to form the basis of future discussions.
Mr Blackford has also written to Mr Corbyn, along with other opposition leaders, to urge him to back another referendum as Labour’s official position.
Plaid Cymru’s Westminster leader, Liz Saville Roberts, said she had approached the meeting in a constructive manner, but told Mrs May: “This must not be a meeting for a meeting’s sake.”
She added: “We are committed to finding a real solution to the Brexit mess. That means taking a no deal Brexit off the table and a People’s Vote on our European future.”
The leader of the Liberal Democrats, Sir Vince Cable, has not spoken publically since his meeting with Mrs May, but earlier he also told the BBC that a no-deal Brexit had to be taken off the table, as well as the PM having a “willingness” to discuss another referendum – which is the party’s preference.
And he echoed calls for Mr Corbyn to support a “People’s Vote”, now that he had lost his no confidence motion, or risk becoming a “handmaiden of Brexit”.