May said she is working to convince Members of Parliament to support the agreement, which has been rejected by the House of Commons twice before.
I continue to believe that the right path forward is for the United Kingdom to leave the European Union as soon as possible with the deal now on the 22 of May, she told Parliament.
She added: But it is with great regret that I have had to conclude that as things stand there is still not sufficient support in the House to bring back the deal for a third meaningful vote.
May said she wants to have a third vote on the deal this week.
I continue to have discussions with colleagues across the House to build support so that we can bring the vote forward this week and guarantee Brexit, she added.
She said that a proposal for MPs to hold votes on alternatives to her deal would set an unwelcome precedent and overturn the balance of our democratic institution.
She also announced that the government will seek to extend the UKs departure date to 11 pm on April 12 with a piece of secondary legislation.
Brexit had been due to go ahead on March 29, when the negotiation period officially ended.
The EU agreed to extend the Brexit negotiation period. EU leaders have proposed that the timeframe is pushed back until April, giving the Prime Minister a chance to secure support for her withdrawal deal.
That deal has been shot down twice in the House of Commons, the lower chamber of UK lawmaking.
If it passes, the EU will allow the UK government until May 23 to implement it but, should it fail, May will have to offer fresh proposals or the UK could face crashing out the bloc without a deal.
The UK electorate narrowly voted to leave the EU in a 2016 referendum.
On Saturday, around one million people packed central London to call for a second referendum on Brexit.
A petition calling for the revocation of Article 50 of the Lisbon Treaty, the official mechanism that May triggered to begin a two-year negotiation period with the EU, has gained more than 5.5 million signatures.
It was the fastest growing petition ever recorded on the UKs Parliaments portal.