LONDON — The British Parliament on Tuesday sought to assert control over Brexit, declaring its opposition to leaving the European Union without a deal and voting to send Prime Minister Theresa May back to Brussels to reopen talks with European leaders.

But the measures are nonbinding and aspirational. They do not guarantee that Britain will get the deal it wants before the scheduled March 29 departure date. In fact, calamity and chaos are still a possible ending.

The vote against a “no-deal Brexit” was a clear defeat for May, whose team had argued that she needed to maintain the threat of leaving the E.U. without an accord to be able to wrest better terms from Brussels.

The no-deal amendment, which passed 318 to 310, was the clearest signal yet that Parliament does not want Britain to leave the trading bloc without a years-long transition period that guarantees smooth trade, an orderly exit and protects the rights of E.U. and British citizens living in Britain and Europe, respectively.

The second amendment, which sends May to Brussels, showed her rebellious Tory lawmakers coming together to back their prime minister. The measure passed 317 to 301.

After the voting, opposition Labour Party leader Jeremy Corbyn agreed to meet with May to discuss how to achieve Brexit. Corbyn had resisted earlier because he wanted the no-deal option first removed from the table.

“It is now clear there is a route that can secure a substantial and sustainable majority in this house for leaving the E.U. with a deal,” May said in the House chamber. “We will now take this mandate forward and seek to obtain legally binding changes.”

As May prepares to pack her bags for Brussels, she faces deeply skeptical European leaders, who have grown weary with her delays and her inability to win approval for the deal they negotiated with her. That deal suffered a humiliating defeat in Parliament two weeks ago.

A spokesman for European Council President Donald Tusk said Tuesday that the withdrawal agreement was “not open for renegotiation.”

The deal painstakingly negotiated between the E.U. and May “is and remains the best and only way to ensure an orderly withdrawal of the United Kingdom from the European Union,” Tusk’s spokesman said.

The Europeans seem in no mood to grant May what she needs to pass a deal, which is a new way for Britain to guarantee that whatever else Brexit yields, it will not mean a return of a hard border — with checkpoints, passport controls and customs inspections — between the Republic of Ireland and Northern Ireland.

The “backstop” provision negotiated with the E.U. — and rejected by Parliament — locks Britain into a European customs regime unless a free-trade deal obviates the need.

May said she would seek “alternative arrangements” to keep the Irish border open and to free Britain from a restrictive European customs regime. But to the frustration of many lawmakers, May and her ministers refused to say what these arrangements might be. 

Labour lawmaker Angela Eagle told Parliament that there was still “puzzlement” after listening to the prime minister for more than an hour. “We are still no nearer any detail on what the phrase ‘alternative arrangements’ [might] mean, except that the prime minister said that they were ‘arrangements’ that were ‘alternative.’ ” 

Northern Irish politician Sylvia Hermann agreed. “The prime minister is trying to encourage this house to vote for an amendment which uses the words ‘alternative arrangements’ to avoid a hard border on the island of Ireland,” she said. “Forgive me, prime minister, if I say those words are nebulous.” 

Even after Tuesday’s votes, Parliament remains in deadlock, without a consensus on how to exit the E.U. after four decades of free trade and shared governance.

The flamboyant, sharp-tongued speaker of the House of Commons, John Bercow, upended tradition by allowing a raft of possible amendments to be debated — leading his critics to charge that the speaker is trying to help backbench renegades foil Brexit by taking control away from the government.

The debate on Tuesday afternoon was heated. 

“Order! The House must behave with decorum!” Bercow bellowed. 

More than a few policymakers in Brussels watched the British debate with mouths agape, noting that it appeared to reflect little about the political realities in the rest of the 27 E.U. member countries. Many of the ideas debated in the House of Commons have already been considered by both British and E.U. negotiators over months of discussions, then discarded because both sides felt they were unworkable.

E.U. leaders and policymakers have repeatedly hammered home that message in conversations with their British counterparts.

The current deal is “the best accord possible and is not renegotiable,” French President Emmanuel Macron told reporters in Cyprus as the British debate got underway. “We must all prepare ourselves” for a chaotic, no-deal Brexit, he said.

The Republic of Ireland’s Europe minister, Helen McEntee, said Tuesday, “There can be no change to the backstop. It was negotiated over 18 months with the U.K. and by the U.K. A bit of realism is needed at this stage.”

Most policymakers in Brussels assume that Britain will soon request to push back the departure deadline, but diplomats say they would need to be convinced that the extra time would go to constructive use before approving it.

Parliament on Tuesday rejected two amendments seeking to delay Brexit if a withdrawal deal is not secured by February. 

Yvette Cooper, a Labour politician who pushed one of those measures, repeatedly asked whether May would consider asking Europe for an extension.

And May, repeatedly, dodged the question. 

May said that she hoped to bring a revised deal back to the House of Commons for a meaningful vote “as soon as we possibly can.” If that hasn’t happened by Feb. 13, the government will make a statement and then give lawmakers a chance to reopen the debate on the way forward, May said.

Other countries have raised concerns about the growing prospect of Britain’s exiting the E.U. without a deal — the default legal position.

On Tuesday, Daniel Coats, the U.S. director of national intelligence, warned a U.S. Senate Intelligence Committee hearing on “worldwide threats” about the potential for Britain to exit the bloc in a disorderly way.

“This would cause economic disruptions that could substantially weaken the U.K. and Europe,” Coats said.

Birnbaum reported from Brussels.