“Now is the time for cool heads. And it is a time to hold our nerve,” she said.
May warned that opposition parties were seeking to exploit last week’s rebuff to derail Brexit altogether.
Her intervention came as Jeremy Corbyn indicated for the first time that he would support a second referendum if the Labour Party conference meeting in Liverpool called for one.
In the statement, May added: “I have said many times that these negotiations would be tough, and they were always bound to be toughest in the final straight.
“But what’s also clear is that many in Labour, the Liberal Democrats and the SNP are trying to thwart Brexit at every step and seeking to exploit this moment for political gain.
“Some are now openly advocating a second referendum and extending article 50 to delay Brexit, sending us right back to square one. Others are talking directly to the EU to actively undermine the UK’s negotiating position.
“But I say, this is the moment to put our country first. This is the moment to set aside our differences and come together in national unity. This is the moment to do what is right for Britain.”
Meanwhile a report in The Sunday Times newspaper claimed that senior members of May’s Downing Street political operation had begun planning for an Autumn poll.
One of the aides was said to have been overheard asking another Tory strategist: “What are you doing in November — because I think we are going to need an election.”
But a Downing Street spokesman said: “It is categorically untrue that No 10 is planning a snap election.”