"Because parliament has made clear it will stop the UK leaving without a deal, we now have a stark choice: leave the European Union with a deal or do not leave at all," May said, as quoted by the Guardian newspaper.
"The longer this takes, the greater the risk of the UK never leaving at all. It would mean letting the Brexit that the British people voted for slip through our fingers. I will not stand for that. It is essential we deliver what people voted for, and to do that we need to get a deal over the line," May underlined.
READ MORE: It is Impossible not to Feel Betrayed Over Brexit
On Friday, the UK prime minister wrote to European Council President Donald Tusk to ask for a Brexit extension until June 30.
Moreover, May would face pressure to step down from her fellow Conservative members of the UK parliament if Brexit delays force the United Kingdom to take part in the elections to the European Parliament, slated for next month, according to the media outlet.
"I and many other Conservatives would prefer leaving the EU on World Trade Organisation terms to any humiliating long extension that forces us to take part in the European elections," Nigel Evans, the executive secretary of the 1922 Committee, a parliamentary group consisting of all Conservative backbencher members of the UK lower house, said.
The UK government and Brussels reached a divorce deal late last year, but the UK parliament has refused to back the agreement and cannot agree on any alternative measures. The country was supposed to have left the bloc on March 29 but missed the deadline.
The European Union gave London until April 12 to either come up with an alternative solution or leave without a deal on that day.