British Prime Minister Theresa May said on Tuesday she would allow parliament to vote on March 14 on whether to delay Brexit if MPs reject both her deal and the prospect of leaving the EU without an agreement.

If those two options are rejected the government would put forward "a motion on whether parliament wants to see a short, limited extension to Article 50," May said, adding that any delay could only be until the end of June.

The prime minister said she still wanted Brexit to happen on the scheduled date of March 29 and repeated her promise to hold a parliamentary vote on her deal on March 12.

If the deal is rejected, as it was overwhelmingly by parliament last month, the government would then hold a vote on March 13 on whether MPs want a no-deal Brexit.

The vote on a possible delay would be the following day.

"Let me be clear, I do not want to see Article 50 extended. Our absolute focus should be on working to get a deal and leaving on March 29," she told parliament.

She added: "I believe that, if we have to, we will ultimately make a success of no deal".

May said her new commitments were a response to MPs who were "genuinely worried about time running out".

Six ministers have threatened to resign in recent days unless May rules out Britain crashing out of the European Union after 46 years with no agreement in place.