Sir Keir Starmer has been urged to submit a formal motion of no confidence in the Tory government.
Scottish National Party ( SNP ) Westminster leader Sir Ian Blackford said now was the time to end the disastrous reign of the Conservatives, and force a confidence vote in the government.
He wrote to the Labour leader that opposition parties couldn't "stand idly by as the Tories attempt to impose their third prime minister in the space of three months".
The SNP and Labour could work together to force through the desperately-needed general election, added Sir Ian.
He told Sir Keir: "It is time to trigger a motion of no-confidence in this disastrous Tory government and - most importantly - it is time for people to have their say in a general election.
"With a vacuum at the top of the Tory leadership, [the time was right to] trigger that motion and attempt to force a general election."
Sir Keir is the only person who can submit a vote of no confidence, as leader of the opposition in the House of Commons.
The submission would result in a Commons debate on the government's ability to continue, with a simple majority needed to pass the motion in the subsequent vote.
Sir Ian added: "I hope we can act together to stop this shambles, put maximum pressure on the Tories as they fight each other, and let the people have their democratic say in a general election.
"Having done so much damage, they simply cannot be allowed to impose a third Tory Prime Minister without an election. It would be unthinkable and undemocratic. Voters must get a say."
However, a confidence vote would be unlikely to pass through the Commons, seeing as the Tories have such a large majority.
If enough Tory MPs decide to turn their backs on the incoming Prime Minister - whoever that might be - Parliament would likely be dissolved, and a general election would be called.
There has previously only been one occasion when a government lost a confidence vote, so it's incredibly rare.
In 1979, Labour's minority government, led by James Callaghan, lost the vote, and was subsequently replaced by the Conservatives' Margaret Thatcher.