Mrs May's comments come as she is warned that accepting a lengthy delay to Brexit would be a "suicide note" for the Tories.
Sunday 7 April 2019 04:36, UK
Theresa May has warned that Brexit could "slip through our fingers" unless a compromise deal can be reached with Jeremy Corbyn.
Her comments come as she continues to try to reach an agreement with the Labour leader that she can get MPs to vote through parliament.
The UK is due to leave the EU on 12 April after her negotiated deal with Brussels was voted down for a third time in the Commons but the prime minister has asked the EU for an extension to 30 June.
The prime minister wants more time to sort out a Brexit deal, but she'll have to get 27 other nations to approve.
Mrs May, who has been accused by Labour of failing to propose changes to her deal in cross-party negotiations, insisted their positions offered "the basis for a compromise".
She said agreeing a deal could lead to the UK leaving the European Union in six weeks but a failure could result in no Brexit at all.
Mrs May said: "Because Parliament has made clear it will stop the UK leaving without a deal, we now have a stark choice: leave the European Union with a deal or do not leave at all.
"My answer to that is clear: we must deliver Brexit and to do so we must agree a deal. If we cannot secure a majority among Conservative and DUP MPs we have no choice but to reach out across the House of Commons.
"The referendum was not fought along party lines and people I speak to on the doorstep tell me they expect their politicians to work together when the national interest demands it.
"The fact is that on Brexit there are areas where the two main parties agree: we both want to end free movement, we both want to leave with a good deal, and we both want to protect jobs.
"That is the basis for a compromise that can win a majority in Parliament and winning that majority is the only way to deliver Brexit.
"The longer this takes, the greater the risk of the UK never leaving at all. It would mean letting the Brexit the British people voted for slip through our fingers.
"I will not stand for that. It is essential we deliver what people voted for and to do that we need to get a deal over the line.
"To achieve this, I will go to Brussels this week to seek a short extension to Article 50. My intention is to reach an agreement with my fellow EU leaders that will mean if we can agree a deal here at home we can leave the EU in just six weeks."
Mr Corbyn wants a customs union to be part of a deal and said he was waiting for Mrs May to move her Brexit "red lines".
He said: "The Labour position is a customs union with the European Union, access to European markets and the retention of regulations for environment, consumers, and workplace rights as a base on which we can build - a dynamic relationship which means we can never fall below them.
"We've set all that out. I haven't noticed any great change in the government's position so far. I'm waiting to see the red lines move."
Tory Eurosceptics reacted furiously to the possibility of Mrs May giving in to Mr Corbyn's demand for a customs union.
Ex-whip Michael Fabricant predicted "open revolt" in the Conservative Party and among Leave voters if Mrs May agreed to the move.
Former Brexit minister Steve Baker hit out at efforts to recruit MPs to sign a "toxic" letter endorsing the PM's cross-party efforts.
Mrs May was warned that accepting a lengthy delay to Brexit would be a "suicide note" for the Conservatives.
Education minister Nadhim Zahawi warned of the "seismic" changes to British politics that would be unleashed if the UK's delayed departure from the EU meant 23 May European Parliament elections went ahead.
Mr Zahawi said the situation needed to be resolved quickly to avoid the "existential threat" posed if the UK remained in the EU at the time of the elections next month.
"It would be, I think, a suicide note of the Conservative Party if we had to fight the European elections," he said.
Meanwhile the Sunday Times reported that Mrs May has a plan to enshrine in law a customs arrangement with the EU in a bid to win over Labour to back a Brexit deal.
Downing Street has not commented on the report.
Pressure is also on Mr Corbyn after 80 MPs told him to secure a guarantee of a second referendum in any deal he agrees with Mrs May.
A letter signed by the MPs, including shadow ministers, was sent to Mr Corbyn and members of the shadow cabinet on Saturday and states that a public vote should be the "bottom line" in the negotiations.
European leaders will decide on Mrs May's request at an emergency Brussels summit on Wednesday.
European Council president Donald Tusk is expected to recommend a longer postponement of one year, with a break clause in the case of earlier ratification, in a so-called "flextension" deal.\