Theresa May has blamed MPs for failing to implement the result of the 2016 EU referendum, and told voters who want Brexit to be over: "I am on your side."
In a televised address from Downing Street, Mrs May said that it was "a matter of great personal regret" for her to have to ask for a three-month delay to Britain's withdrawal from the EU, which was due to take place on March 29.
She will go to Brussels on Thursday to make a formal request to the other 27 EU leaders for an extension to the two-year Article 50 negotiation process.
Earlier, European Council president Donald Tusk said he believed a short delay "would be possible" after he spoke to the Prime Minister by phone.
But he said that the extension - which must be agreed unanimously by the EU27 - was likely to be conditional on Mrs May succeeding in forcing her twice-rejected Brexit deal through Parliament.
The PM made the request in a letter to Mr Tusk exactly 1,000 days after the 2016 referendum which delivered a 52%-48% majority to quit the EU.
Speaking behind a lectern in 10 Downing Street, Mrs May said that MPs - who rejected her deal by 230 votes in January and 149 last week - had been "unable to agree on a way to implement the UK's withdrawal".
And in a message directed at voters, she added: "Of this, I am absolutely sure: You the public have had enough.
"You are tired of the infighting, you're tired of the political games and the arcane procedural rows, tired of MPs talking about nothing else but Brexit when you have real concerns about our children's schools, our National Health Service, knife crime.
"You want this stage of the Brexit process to be over and done with. I agree. I am on your side. It is now time for MPs to decide."