In a video clip published on Twitter, the Prime Minister appeared to confirm that she would not try to put her existing deal to another vote in the House of Commons.
"Where we are at is that the Government negotiated a deal with the EU and my preference was for that deal to be passed by Parliament and we could leave the EU on that basis," she said.
"But Parliament's now rejected that deal three times and right now, as things stand, I can't see them accepting it.
"But at the same time Parliament has also said that they don't want us to leave without a deal, with no-deal. Indeed, [last] week, Parliament's been legislating to block no-deal.
"So the choice that lies ahead of us is either leaving the European Union with a deal or not leaving at all."
May said the UK "absolutely must leave the European Union" and the intransigence of some of her own MPs who remain opposed to her deal meant there was no choice but to hold cross-party talks with Labour.
She said: "When you think about it, people didn't vote on party lines when it came to the Brexit referendum, and you know I think often that members of the public want to see their politicians working together more often.
"There's lots of things on which I disagree with the Labour Party on policy issues. But on Brexit I think there are some things we agree on.
"Ending free movement, ensuring we leave with a good deal, protecting jobs, protecting security and so we're talking, can we find a way through this that ensures that we can get a good deal and a deal agreed through Parliament.
"It'll mean compromise on both sides, but I believe that delivering Brexit is the most important thing for us."
May said MPs had a "duty" to deliver on the 2016 EU referendum result.
"I want to do that in a good way, that doesn't disrupt people's lives, that protects jobs, protects out security, protects the United Kingdom," she said.
"That's what the Government is working for."
Cross-party talks to jumpstart plans for Brexit are expected to resume before the UK's Saturday deadline for leaving the EU.
While Corbyn has faulted the Government, saying it showed no willingness to budge from its previous Brexit positions, Labour business minister and negotiator Rebecca Long-Bailey held out hope and said further talks are expected.
The discussions' "overall mood is quite a positive and hopeful one" despite the Government's "disappointing" failure to shift its stance on several issues, she said.
"The sad thing is at the moment, we haven't seen overall any real changes to the deal, but we are hopeful that will change in coming days, and we are willing to continue the talks as we know the government are," Long-Bailey told the BBC.
"We are currently waiting for the government to come back to us now to state whether they are prepared to move on any of their red lines," she added.
Long-Bailey insisted that Labour wants to avoid a no-deal Brexit "in any situation" and was prepared to cancel Brexit rather than see Britain crash out of the EU with no agreement in place, an outcome expected to wreak havoc on businesses and disrupt travel throughout Europe.
But Conservative MP Andrea Leadsom said a no-deal scenario wouldn't be "nearly as grim as many would advocate."
She said the governing party was working "through gritted teeth" with Labour to find a compromise, but its bottom line is Britain leaving the EU.
May has asked the remaining EU countries for another postponement that would extend to June 30, hoping to secure an alternative deal from the opposition negotiations and Parliament in a matter of weeks.
Other European leaders are expected to respond to the delay request during a summit in Brussels scheduled for Thursday.
- Additional reporting AP
