The prime minister wrote a letter to MPs following her return from talks with European Union (EU) leaders in Brussels and outlined a “clear choice” made up of four options.
Ms May appeared to immediately rule out one of them – revoking Article 50 and remaining in the EU - as a “betrayal” of the referendum result.
She also seemed to accept that leaving with no deal on the new Brexit date of 12 April was not supported by MPs.
The remaining options, she said, were to back her Brexit deal and leave on 22 May or ask the EU for another extension – which would mean holding elections for British representatives to the European Parliament.
Ms May also attempted to reach out to MPs following criticism of her Wednesday night speech during which she appeared to blame them for the UK’s failure to leave the EU on 29 March.
Labour’s Wes Streeting had accused the prime minister of putting MPs’ lives in danger with an “incendiary” address while Anna Soubry said she “can’t go home” this weekend because of death threats.
Ms May told MPs: “I expressed my frustration with our failure to take a decision, but I know that many of you are frustrated too. You have a difficult job to do and it was not my intention to make it any more difficult. People on all sides of the debate hold passionate views and I respect those differences.
“I would like to thank all of those colleagues that have supported the deal so far and also those that have taken the time to meet me to discuss their concerns.”
The prime minister travelled to Brussels in the hope of extending Article 50 until 30 June but EU leaders ultimately agreed that the UK could have an unconditional extension until 12 April, and a further extension until 22 May if MPs approved the withdrawal agreement next week.
In her letter to MPs, Mrs May wrote: ”The Council’s decisions mean we have a clear choice: 1. We can revoke Article 50 – but that would be to betray the result of the referendum. 2. We can leave with no deal on 12 April – but the House has previously said this is not something it will support. 3. If it appears that there is not sufficient support to bring the deal back next week, or the House rejects it again, we can ask for another extension before 12 April – but that will involve holding European Parliament elections. 4. If it appears that there is sufficient support and the Speaker permits it, we can bring the deal back next week and if it is approved we can leave on 22 May.”
Additional reporting by Press Association