Theresa May has said MPs have "one last chance" to deliver Brexit, urging them to back what she said was a "new deal", ONA reports citing BBC.
MPs will get a vote on whether to hold another referendum if they back the EU Withdrawal Agreement Bill, she said.
The bill also contains new guarantees on workers' rights, environmental protections and the Northern Irish border, as well a customs "compromise".
Labour said it was a "rehash" of existing plans and Tory Brexiteers took to social media to vent their anger.
Jacob Rees-Mogg said what was on offer was "worse than before", while Zac Goldsmith said the bill was a "convoluted mess" and the prime minister - who has offered to quit once a Brexit agreement is approved by Parliament - should leave now.
MPs have rejected the withdrawal agreement negotiated with the EU three times and attempts to find a formal compromise with Labour also failed.
In what is seen as a last roll of the dice, Mrs May is now bringing the Withdrawal Agreement Bill - legislation required to bring the agreement into UK law - to Parliament in early June.
In a speech in London, the PM implored MPs to come together, saying a negotiated exit from the EU would be "dead in the water" if they rejected the plan.
"I have compromised, now I ask you to compromise too," she said, adding that she had even "offered to give up the job I love earlier than I would like".
Mrs May said the deadlock over Brexit was having a "corrosive" impact on political debate in the country and was stopping progress in other areas.
"The majority of MPs say they want to deliver the result of the referendum... and I believe there is now one last chance to do that," she said.
"We are making a new offer to find common ground in Parliament. That is the only way to deliver Brexit."
The key points of the PM's revised plan are:
A guarantee of a Commons vote on whether to hold another referendum on the government's Brexit deal, with a promise to honour the outcome
A vote on different customs options, including a government proposal for a temporary customs union for goods - what Mrs May called a "customs compromise"
A legal obligation for the UK to come up with an alternative to the Northern Ireland backstop by the end of 2020
If the backstop does come into force, the bill would guarantee Northern Ireland remains aligned with the rest of the UK and remains in same customs territory
Legislation to ensure workers rights are "every bit as good if not better" after Brexit and guarantees of no dilution in environmental standards
A legal duty to seek changes to the political declaration on future relations with the EU
While she personally opposed another referendum on the terms of Brexit, the PM said she recognised the "genuine and sincere" feelings on the issue in Parliament.
She urged MPs to back the Withdrawal Agreement Bill at its first parliamentary hurdle in June and then "make the case" for another public vote when the bill was examined in detail later.