UK Prime Minister Theresa May has seen off a bid to remove her government from power, winning a no confidence vote by 325 to 306.
Rebel Tory MPs and the DUP - who 24 hours ago rejected the PM's Brexit plan - voted to keep her in Downing Street.
Labour leader Jeremy Corbyn argued that Mrs May's "zombie" administration had lost the right to govern.
Mrs May said she would start talks with other party leaders to find a Brexit compromise that MPs will back.
Giving her reaction to the result, Mrs May told MPs she would "continue to work to deliver on the solemn promise to the people of this country to deliver on the result of the referendum and leave the European Union".
She invited leaders of all parties to have individual meetings with her on the way ahead for Brexit - starting tonight with offers made to the Westminster leaders of Labour, the Liberal Democrats, the SNP and Plaid Cymru - but called on them to approach them with a "constructive spirit".
"We must find solutions that are negotiable and command sufficient support in this House," she added.
But Mr Corbyn, who tabled the no confidence motion, said that before any "positive discussions" could take place, the prime minister should rule out a no-deal Brexit.
"The government must remove clearly, once and for all, the prospect of the catastrophe of a no-deal exit from the EU and all the chaos that would come as a result of that," he told MPs.
Mr Corbyn's no confidence motion was backed by all the opposition parties, including the Scottish National Party and the Liberal Democrats.
His party has not ruled out tabling further no confidence motions - but Mr Corbyn is under pressure from dozens of his own MPs and other opposition parties to now get behind calls for a further EU referendum instead.
The leader of the SNP in Westminster, Ian Blackford, welcomed the offer of talks from the prime minister, saying it was important for all parties to "recognise the responsibility that we have" after Mrs May's original deal was voted down.
He committed his party to "work constructively with the government".
But he said extending Article 50, the legal mechanism taking the UK out of the EU on 29 March, a further referendum and the avoidance of a no-deal Brexit all "have to be on the table".
The leader of the Liberal Democrats, Vince Cable, said it would be "silly not to talk", but he also said no deal 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.
Sir Vince also reiterated his calls from Jeremy Corbyn to get behind the "People's Vote" too now that he had lost his no confidence motion.
"He has now got to change his position and come behind the 'People's Vote' or he will just be seen, and will be, a handmaiden of Brexit," he told BBC News.
Plaid Cymru's Westminster Leader, Liz Saville Roberts, and the party's Brexit spokesman, Hywel Williams, confirmed they would meet Mrs May at 21:00, but their view is the "only way to break the deadlock" is for another referendum.
The leader of the DUP in Westminster, Nigel Dodds, said the result showed the importance of the confidence and supply arrangement between his party and the Conservatives.
After the 2017 election, the Tories agreed a financial package with the DUP in exchange for support on certain issues, giving them a working majority in Parliament.
He said the agreement was "built on delivering Brexit" and that he was looking forward to "working in the coming days to achieve that objective".
How have Tory MPs reacted?
The Conservatives showed unity over the confidence vote, with all 314 members able to vote backing the PM.
But there are still divisions within the party over the way forward with Brexit.
The Prime Minister's official spokesman said she would meet with Eurosceptic MPs from her own benches on Thursday to discuss proposals.
When asked about the possibility of pursuing a customs union with the EU - the proposal that Labour supports - Work and Pensions Secretary Amber Rudd told Politics Live that "everything should be on the table".
During her statement, Mrs May reiterated a promise to return to the Commons on Monday to give MPs another vote on her plans.
"The House has put its confidence in this government," she said.
"I stand ready to work with any member of this House to deliver Brexit and ensure that this House retains the confidence of the British people."