She is not prepared to delay Brexit any longer than 30 June, the fact we are not leaving on the 29 March "is a matter is of great personal regret to me".
Mr Juncker told German radio that a short extension would give the UK Parliament time to agree to the existing withdrawal agreement text, but insisted there would be "no more negotiations".
She added: "I'm still working on ensuring that Parliament can agree a deal so that we can leave in an orderly way".
A vote is not likely to take place until next week.
"I voted against a delay and I fully understand the public's frustration with the current situation - the sooner we leave, the sooner we can get on with negotiating our own trade negotiations".
And anti-Brexit campaigners haven't abandoned the idea of a new referendum on remaining in the EU.
He said that if MPs approve the Brexit deal, there was no need for another "extraordinary" summit next week.
Image copyright AFP Image caption What will European Union leaders do if UK MPs reject the deal for a third time?
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"I have therefore this morning written to President Tusk, the president of the European Council, informing him that the United Kingdom seeks an extension to the Article 50 period until the 30th June", she said.
May has also said that if her deal is not passed, parliament will "have to decide how to proceed".
His words come after South West Norfolk MP Liz Truss was one of seven Cabinet ministers who voted against the Prime Minister's motion to delay Brexit last Thursday.
Theresa May will not request a long delay to Brexit from European leaders, Downing Street says.
Media reports in London said that at a private meeting with leaders of political parties ahead of her statement, she ruled out an option of calling a snap election.
"What matters is that we recognise that Brexit is the decision of the British people".
"In the light of the consultations I have conducted over the past days, I believe a short extension will be possible but it will be conditional on a positive vote on the withdrawal agreement in the House of Commons", Tusk told reporters.
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"It is high time we made a decision", May said, telling Britons: "I am on your side".
Emmanuel Macron has warned Britain is heading for a no-deal Brexit unless the House of Commons ratifies the withdrawal agreement negotiated with Brussels.
"All MPs have been willing to say is what they do not want", she complained, in a televised address that sought to reach over the heads of parliament to the British people and infuriated lawmakers on both sides of the House of Commons.
An online petition urging the government to cancel Brexit has gained more than 1 million signatures and crashed earlier in the day when it attracted so much traffic.
As Brexit is sapping EU resources, the leaders will also turn to other pressing issues, including the state of their economies, ties with China, and ringfencing the European elections from illegitimate interference. "In the case of a negative vote in Britain, we will be going towards no-deal".
European Council President Donald Tusk said it would be possible to grant Britain a short postponement if parliament next week backs May's divorce agreement, which it has already voted down twice.
Mrs May is hoping a third vote could be admitted despite the speaker's decision, if she can formalise changes made to the agreement with European Union leaders last week.
"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".
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