LONDON — After an embarrassing setback in Parliament, Prime Minister Theresa May toured European capitals on Tuesday, meeting with leaders and looking for some way to shore up support back home for her imperiled agreement on Britain’s withdrawal from the European Union.

British lawmakers had been scheduled to vote on the agreement on Tuesday, but after a debate in which it came under attack not only from the opposition but also from many members of her own Conservative Party, Mrs. May delayed the vote on Monday, acknowledging that her plans had faced defeat “by a significant margin.”

Her retreat undermined the tenuous hold on power by a prime minister whose opponents, both inside and outside her party, have been speaking openly about trying to topple her. It also left Britain’s exit from the European Union, or Brexit, in limbo, with lawmakers and analysts alike saying it was anyone’s guess what would happen next.

Jeremy Corbyn, leader of the opposition Labour Party, suggested on Tuesday that he would try to bring down the government through a vote of no confidence, but refused to say when. Leaders of several smaller opposition parties this week urged Mr. Corbyn to make a no-confidence motion, vowing to support it.