Boris Johnson is to try again for a 12 December general election after MPs rejected the plan.
The prime minister will publish a short piece of legislation seeking the support of the Lib Dems and SNP for an election on that date.
It came after he failed to secure the necessary support of two-thirds of MPs under the Fixed Terms Parliament Act.
“This House can no longer keep this country hostage,” he told MPs, saying Parliament had become “dysfunctional”.
The government comfortably won Monday’s vote by 299 votes to 70 – after the Labour frontbench abstained.
However, it fell well short of getting the support of the 434 MPs it needed.
But the PM said he would persist with his efforts to get an early election, telling MPs that “one way or another” the current deadlock had to be broken.
The new legislation he is proposing would only require the support of a simple majority of MPs able to vote, which would be 320.
The Lib Dems and SNP are offering to back an election on Monday, 9 December instead, which they say will prevent any chance of the PM’s Brexit deal being approved in the short time before Parliament is dissolved.
They have proposed their own short bill and it remains to be seen whether they will support the government’s legislation, which No 10 has said will be “almost identical”.
Negotiations between the two sides over a compromise date are reportedly taking place in Westminster.
The SNP’s Westminster leader Ian Blackford said he did not “trust” the PM and he wanted reassurances from Mr Johnson would try to bring back his Brexit agreement back for approval.
Mr Johnson said they was not the support for the Withdrawal Agreement Bill – which has been in limbo since MPs last week rejected the PM’s timetable to push it through the Commons by the now lapsed 31 October deadline.
Following Monday’s vote, Mr Johnson suggested the electorate would be “absolutely bewildered” by Labour leader Jeremy Corbyn’s apparent resistance to an election.
But the Labour leader said he would only support an election once his conditions were met.
The one-line bill being proposed by the government could be amended by MPs, potentially to allow 16 and 17-year olds to vote. If that happened, the government could abandon the bill.
Although the Lib Dems and SNP back the principle of reducing the voting age, Lib Dem leader Ms Swinson said stopping Brexit was the priority for younger voters.