Theresa May has asked MPs to make an "honourable compromise" as she seeks to persuade them to back her Brexit deal at the third time of asking.
Writing in the Sunday Telegraph, the prime minister said failure to support the deal would mean "we will not leave the EU for many months, if ever".
Mrs May is expected to bring her withdrawal agreement back to the Commons next week for a third vote.
It comes after MPs this week rejected her deal and voted to delay Brexit.
The EU will decide the terms and conditions of any extension. Legally, the UK is still due to leave the EU on 29 March.
Meanwhile, Labour leader Jeremy Corbyn has written to MPs across the Commons inviting them for talks to find a cross-party compromise.
Mrs May says if Parliament votes for her withdrawal deal before an EU leaders' summit on Thursday, the UK will seek a short delay to Brexit to pass the necessary legislation.
"That is not an ideal outcome - we could and should have been leaving the EU on March 29," she said.
"But it is something the British people would accept if it led swiftly to delivering Brexit. The alternative if Parliament cannot agree the deal by that time is much worse."
If a deal is not agreed before Thursday, EU leaders are contemplating a much longer delay.
Mrs May said it would be a "potent symbol of Parliament's collective political failure" if a delay to Brexit meant the UK was forced to take part in May's European elections - almost three years after voting to leave the EU.