Theresa May has declared it is time for "finding a way forward" with Brexit after surviving a no confidence vote in her government.
The Prime Minister invited MPs from all parties to try to achieve a breakthrough on Brexit saying it was time to "put self interest aside."
She said it was disappointing Jeremy Corbyn had not agreed to meet for talks.
Speaking in Downing Street on Wednesday night, Mrs May said: "This evening the Government has won the confidence of Parliament.
"Overwhelmingly, the British people want us to get on with delivering Brexit.
"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."
She said she had held "constructive" meetings with party leaders and would meet MPs including the DUP on Thursday.
She added: "I am disappointed that the leader of the Labour Party has not so far chosen to take part, but our door remains open."
Mrs May survived Mr Corbyn's attempt to oust her as Prime Minister, as MPs rejected his motion of no confidence in the Government by a margin of 325 to 306.
The Prime Minister's 19-vote victory came less than 24 hours after the crushing defeat of her EU Withdrawal Agreement in the House of Commons, and clears the way for her to start cross-party talks on a Brexit Plan B.
In the speech, Mrs May also aimed remarks at Parliamentarians who voted against her Brexit plan on Tuesday, saying that "MPs have made clear what they don't want, we must all work constructively together to set out what Parliament does want".
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She added: "It will not be an easy task, but MPs know they have a duty to act in the national interest, reach a consensus and get this done.
"In a historic vote in 2016 the country decided to leave the EU. In 2017, 80% of people voted for parties that stood on manifestos promising to respect that result.
"Now, over two-and-a-half years later, it's time for us to come together, put the national interest first - and deliver on the referendum."
Conservative rebels and members of the Democratic Unionist Party who consigned the PM to the worst defeat in parliamentary history had rallied behind her to see off the threat of a general election.
Welcoming the result, Mrs May told the Commons: "I am pleased that this House has expressed its confidence in the Government.
"I do not take this responsibility lightly and my Government will continue its work to increase our prosperity, guarantee our security and to strengthen our union.
"And yes, we will also continue to work to deliver on the solemn promise we made to the people of this country to deliver on the result of the referendum and leave the European Union."
The SNP's Westminster leader has written to the Prime Minister saying cross-party talks about a future Brexit deal must have a second referendum on the table to have any meaning.
Ian Blackford said "cosmetic changes" to her EU withdrawal agreement were no long an option after it was defeated in Parliament.
Mrs May held meetings with him and other leaders about holding cross-party discussions over a future deal, having survived the confidence vote on Wednesday.
Following those talks, he wrote to Mrs May saying: "For us to enter into that discussion there needs to be a clear indication of willingness on the side of the government for these to be genuine negotiations.
"That requires a clear gesture of good faith by you and your government.
"Discussions around cosmetic changes to your deal, which has now been rejected by Parliament will not move this matter forward.
"It is my view that if you are able to confirm that the extension of Article 50, a ruling out of a No Deal Brexit and the option of a second EU referendum would form the basis of those discussions, then we could participate in them.
The SNP has also written a cross-party letter with the Liberal Democrats, Plaid Cymru and the Greens to Labour leader Mr Corbyn.
It argues that "now that the Government and the Official Opposition's options have been tested before the House, we believe the only way now which presents a real chance of breaking the Brexit deadlock is to put the decision to the people by backing a People's Vote".