She told lawmakers Britain still has options including an extension that would require taking part in European Parliament elections in May.
Many carried blue and yellow EU flags or were dressed in these colours, while others carried Union Jack flags.
The EU believes a "no-deal" Brexit is increasingly likely.
A similar amendment voted on earlier this month lost by just two votes so this is expected to have a good chance of passing.
After three years of tortuous debate, it is still uncertain how, when or even if Brexit will happen as Mrs May tries to plot a way out of the nation's gravest political crisis in at least a generation.
As the final Brexit deadlines loom, the prospect of an imminent no-deal scenario has become more real.
Finance Minister Philip Hammond, too, said a change of prime minister would not break the impasse, though he acknowledged it may be impossible for parliament to back May's plan.
Conservative Dominic Grieve said: "The vote last week was not a serious vote, it was always apparent when it was moved that there were large numbers of MPs who might support it who didn't think it was the right moment to take place, so I don't think one should make a judgement on its viability like that". The premier's office is so far not committing to allow Tories this liberty, potentially sparking another revolt from her ministers in her Cabinet.More news: Ex-Justice Official Fears 'Whitewash' In Barr Rejection Of Trump Obstruction Charges
"The alternative is to pursue a different form of Brexit or a second referendum".
Proposed by opposition Labour lawmaker Yvette Cooper and supported by more than 30 lawmakers, including Conservatives, it calls on the government to set out by the end of March 28 - if parliament has not approved May's deal by then - how it will ensure Britain does not leave the European Union on April 12 without a deal. May went to her usual church service near her Chequers country residence on Sunday with her husband.
Prime Minister Theresa May has said she will ditch plans for another vote on her Brexit deal if enough MPs don't support it.
An effigy of British Prime Minister Theresa May is wheeled through Trafalgar Square during a Peoples Vote anti-Brexit march in London, March 23, 2019.
The Sunday Times reported that May's de-facto deputy, David Lidington, was one contender to be interim prime minister but others are pushing for Environment Secretary Michael Gove or Foreign Secretary Jeremy Hunt.
Downing Street told CNN that it would not comment on speculation from newspapers, and that the rumors have not affected the schedule for the upcoming week.
Speaking on Sky's "Sophy Ridge on Sunday", the chancellor reiterated that it was up to lawmakers to come together to find a way forward if they continue to reject May's deal, and that the government would give them time to do that in coming days. Brendan, 50, from Tooting, London, said that he found it hard explaining to his two daughters why the country was leaving the EU.
When presented with a list of possible options, he ruled out a no-deal exit or revoking Article 50 - which is the formal notification to the European Union - but he was less equivocal about the prospect of a second vote. Hammond's comments could enrage anti-EU members of May's party, who - along with the prime minister herself - have argued against another vote.