The move came after Johnson accused anti-Brexit U.K. politicians of collaborating with the EU to stymie Britain's exit from the bloc.
Jeremy Corbyn, who heads the main opposition Labour Party, said he planned to call a no-confidence vote in Johnson's government "at the earliest opportunity when we can be confident of success" once Parliament returns from its summer break in September.
In a letter to other opposition leaders and pro-EU Conservative lawmakers, the Labour chief said Parliament should then unite behind a Corbyn-led "temporary government" that would seek a delay to Brexit day - currently scheduled for Oct. 31 - and call a national election.
The plan is feasible under Parliament's rules, but is likely to face resistance. The smaller opposition parties agree on the need to avoid a no-deal Brexit, but don't want to put Corbyn - a veteran left-winger whom many distrust - in power. Labour, meanwhile, is likely to oppose a politician from any other party heading a national unity government.
Johnson has vowed that Britain will leave the EU on Oct. 31 - just 11 weeks away - with or without a divorce deal. He is demanding the EU make major changes to the agreement the bloc made with his predecessor, Theresa May. The EU refuses to renegotiate, so a no-deal Brexit appears increasingly likely.
Johnson claimed Wednesday there was "a terrible kind of collaboration" between an intransigent EU and U.K. politicians who want to prevent Brexit.
"We need our European friends to compromise, and the more they think there's a chance Brexit can be blocked in Parliament the more adamant they are of sticking to their positon," Johnson said during a question-and-answer session on Facebook.
Many economists say leaving the EU without an agreement on the terms will trigger a recession and cause economic mayhem, with shortages of fresh food and other goods likely as customs checks snarl Britain's ports.
Johnson and other Brexit supporters argue that any short-term turbulence will be outweighed by new economic opportunities once Britain leaves the 28-nation bloc and can strike trade deals around the world - notably with the United States. Critics note that the EU accounts for almost half of Britain's trade and any new trade deals are likely years away.
Philip Hammond, who was Britain's Treasury chief until three weeks ago, accused Johnson on Wednesday of steering the country toward a damaging no-deal Brexit that isn't backed by Parliament or British voters.
Hammond, a Conservative legislator who stepped down as finance minister just before Johnson became prime minister last month, told the BBC that Johnson had moved from a tough negotiating stance to a "wrecking" one by insisting on changes to the withdrawal agreement between Britain and the EU that the bloc would not accept.
He said while he believed Johnson wanted a deal, "there are other people around him whose agenda is different" - an apparent reference to advisers such as Dominic Cummings, one of the architects of the country's 2016 decision to leave the EU.
Hammond criticized Johnson's government for perpetuating "myths" that the British people voted for a no-deal Brexit and that leaving the EU without a negotiated settlement would be painless.
"There is no mandate for leaving with no deal," Hammond said, adding that "during the referendum campaign there was virtually no mention made by the leaders of that campaign at all of the possibility of leaving with no deal."
Johnson has refused to rule out suspending Parliament if legislators try to delay or prevent Brexit in the fall. Hammond said that would "provoke a constitutional crisis."
House of Commons Speaker John Bercow, who controls the day-to-day business of Parliament, said he would seek to prevent the prime minister from overriding Parliament.
"If there is an attempt to circumvent, to bypass or - God forbid - to close down Parliament, that is anathema to me," Bercow told the Edinburgh Fringe Festival in comments reported by the Herald newspaper. "I will fight with every breath in my body to stop that happening."
Follow AP's full coverage of Brexit and British politics at: https://www.apnews.com/Brexit
Copyright 2019 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.