May insisted she intends for Britain to leave as planned in a little more than a month.
May has steadfastly argued that she must keep the prospect of Britain crashing out the bloc without an agreement on March 29 on the table in order to wrest essential concessions from Brussels.
"He has gone back on his promise to respect the referendum result and now wants to hold a divisive second referendum that would take our country right back to square one", she said.
Labour's Brexit spokesman, Keir Starmer, said the public should be given a vote on whether to accept Mrs May's deal or to remain in the EU.
May said that if Parliament rejects her deal with the European Union in a vote due by March 12, lawmakers would be given a vote the next day on whether to leave the bloc without a withdrawal agreement.
Plaid Cymru's Jonathan Edwards said it would be the "political equivalent of swimming around in circles" if Brexit is extended but no deal comes back on the table later in the year.
It follows days of speculation that Labour might be moving towards backing a public vote.
The prospect of holding a second vote poses a dilemma for Corbyn; while numerous party's members and supporters fervently back a so-called People's Vote, others simply want Britain to leave the European Union as soon as possible.
Mr Howlin made the comments after the British Labour Party announced it would be prepared to back a new referendum if its withdrawal plan is rejected by MPs in Westminster this week. It is likely to cheer many party members, who have backed calls for a so-called "people's vote".
Train to nowhere: 183 passengers stuck on Amtrak train since Sunday
What next: The train was originally stuck about 45 miles southeast of Eugene, Oregon , according to the Oregonian . They reiterated Amtrak's decision to keep passengers on the train, noting there was limited lodging in Oakridge.
Former Labour frontbencher Owen Smith was sacked past year for his support for a second referendum. It would require the support of numerous lawmakers from the governing Conservative Party, for example.
Delaying Brexit has the potential to split May's Cabinet and her ruling party, triggering a rebellion from Brexit-supporting Tories who might even try to bring down her government. Brexit has proved to be such a divisive issue that both mainstream parties have suffered defections.
The Bank of England also forecast in November that a no-deal Brexit in March would cause the United Kingdom economy to shrink by about 8% within a year, the worst drop the country has seen since the 1920s.
On Tuesday morning, Ms James told BBC Radio 4's Today programme that Mrs May needs to rule out the "catastrophe" of a no-deal Brexit by extending Article 50 if she is unable to secure parliamentary support for her Withdrawal Agreement.
"I don't see how businesses can plan".
"That's why, in line with our conference policy, we are committed to also putting forward or supporting an amendment in favour of a public vote to prevent a damaging Tory Brexit being forced on the country".
He said: "I have lost count of the number of times the Prime Minister has come to this House to explain a further delay".
Guto Bebb said more time would be needed to pass legislation for a deal.
She didn't just say once that she would never countenance a delay in Brexit, and that Britain will definitely leave on 29 March. May refused to say how long it might last, indicating only that she'd like any delay to be "as short as possible". When asked repeatedly if May was going to delay, Lidington did not address the questions directly.
Dutch Prime Minister Mark Rutte warned her against "sleepwalking" into a chaotic Brexit next month.