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, youre 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 childrens 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.
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.
Former Ukip leader Nigel Farage described the speech as appalling and pathetic, adding: The Brexit betrayal is hers.
Conservative MP Andrea Jenkyns criticised the Prime Ministers statement, saying it said very little and encouraged her to ensure that Brexit happens on March 29 regardless of Parliament.
She tweeted: As usual another statement saying very little. PM says she regrets having to delay. Then dont do it!
It is in the Prime Ministers power to ensure we leave on the 29th, regardless of what Parliament suggests.
Fellow Conservative Conor Burns tweeted in response to the speech: What was actually the point of that?
After speaking to May on Wednesday evening, Labour leader Jeremy Corbyn said: The Prime Minister has shown tonight she is in complete denial about the scale of the crisis we are facing and unable to offer the leadership the country needs.
To continue to bring back her damaging and twice rejected deal without significant changes, while threatening a no deal outcome ruled out by MPs, is unacceptable and reckless.
I made clear to the Prime Minister tonight that we must move immediately to agree a compromise alternative that supports jobs and living standards, can win the support of parliament, be negotiated with the EU and bring the country together.
Theresa May's speech in full:
Nearly three years have passed since the public voted to leave the European Union.
It was the biggest democratic exercise in our countrys history.
I came to office on a promise to deliver on that verdict.
In March 2017 I triggered the Article 50 process for the UK to exit the EU and Parliament supported it overwhelmingly.
Two years on, MPs have been unable to agree on a way to implement the UKs withdrawal.
As a result, we will now not leave on time with a deal on the 29th of March.
This delay is a matter of great personal regret for me.
And of this I am absolutely sure: You, the public, have had enough.
Youre tired of the infighting, youre 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 childrens 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.
So, today, I have written to Donald Tusk the President of the European Council to request a short extension of Article 50 up to the 30th of June to give MPs the time to make a final choice.
Do they want to leave the EU with a deal which delivers on the result of the referendum, that takes control of our money borders and laws while protecting jobs and our national security?
Do they want to leave without a deal, or do they not want to leave at all causing potentially irreparable damage to public trust not just in this generation of politicians but to our entire democratic process?
It is high time we made a decision.
So far, Parliament has done everything possible to avoid making a choice.
Motion after motion and amendment after amendment has been tabled without Parliament ever deciding what it wants.
All MPs have been willing to say is what they do not want.
I passionately hope MPs will find a way to back the deal Ive negotiated with the EU, a deal that delivers on the result of the referendum and is the very best deal negotiable.
And I will continue to work night and day to secure the support of my colleagues, the DUP and others for this deal.
But I am not prepared to delay Brexit any further than the 30th of June.
Some argue that Im making the wrong choice and I should ask for a longer extension to the end of the year or beyond to give more time for politicians to argue over the way forward.
That would mean asking you to vote in European elections nearly three years after our country decided to leave.
What kind of message would that send? And just how bitter and divisive would that election campaign be at a time when the country desperately needs bringing back together.
Some have suggested holding a second referendum.
I dont believe thats what you want and it is not what I want.
We asked you the question already and youve given us your answer.
Now you want us to get on with it.
And that is what I am determined to do.
Earlier, European Council president Donald Tusk said he believed a short delay would be possible after he spoke to May following her formal request for an extension of the Article 50 withdrawal process to the end of June.
However, he stressed that the EU would only accept the delay if MPs accepted Mays deal.
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.
The leaders of the Labour Party, SNP, Liberal Democrats, Green Party, Plaid Cymru and the Independent Group are understood to have been invited to meetings with May.
Jeremy Corbyn refused to take part in opposition party talks because members of the breakaway Independent Group were present, other leaders said.
Liberal Democrat leader Sir Vince Cable said: That is rather a strange way to behave in a national crisis.
Chuka Umunna, spokesman for The Independent Group, said: I find it extraordinary behaviour in a national crisis.
Mr Tusk, a former Polish prime minister, told a press conference in Brussels: In the light of the consultations that I have conducted over the past days, I believe that a short extension would be possible.
But it would be conditional on a positive vote on the Withdrawal Agreement in the House of Commons.
The question remains open as to the duration of such an extension.
Tusk indicated that it should be possible for leaders of the remaining EU 27 to approve his plan at a summit in the Belgian capital starting on Thursday.
He said that while he did not foresee the need for another extraordinary summit next week, he would not hesitate to call one if necessary.
Tusk continued: If the leaders approve my recommendations and there is a positive vote in the House of Commons next week, we can finalise and formalise the decision on extension in the written procedure.
However, if there is such a need, I will not hesitate to invite the members of the European Council for a meeting to Brussels next week.
Tusk added: Even if the hope for final success may seem frail, even illusory, and although Brexit fatigue is increasingly visible and justified, we cannot give up seeking until the very last moment a positive solution – of course without opening up the Withdrawal Agreement.
We have reacted with patience and goodwill to numerous turns of events and I am confident that also now we will not lack the same patience and goodwill at this most critical point in this process.
Earlier, during a stormy session of Prime Ministers Questions, May sparked speculation that she may step down if either MPs or Europe demand a longer extension to the Article 50 negotiation process.
As Prime Minister, I am not prepared to delay Brexit any further than June 30, she said.
If the delay is approved by the EU leaders, May will rush legislation through both Houses of Parliament next week to remove the March 29 leaving date from Brexit laws.
She told MPs she intends to table her Withdrawal Agreement for a third time in the Commons, in the hope of overturning massive defeats inflicted on it in January and March.
Aides declined to name a date for the third meaningful vote – known in Westminster as MV3 – but said it would happen as soon as possible.