Ruth Davidson, the Scottish Conservative leader who is likely to play a key role for the Unionists in any future referendum, replied: "Responding to anonymous tittle-tattle by trading mandates over Twitter? Goodness. Someone's gone the full Donald Trump ... "
In the Commons, May used a question-and-answer session over her visit to the European Council last week to aim her own waspish comments at Sturgeon.
She said: "This is not a moment for playing political games. It is a moment to bring our country together to honour the will of the British people and to shape for them a better, brighter future and a better Britain."
She added: "The evidence in Scotland is that actually the majority of the Scottish people do not want a second independence referendum."
Asked whether she had come across support for an independent Scotland joining the EU on a visit to Brussels last week, May said: "I did not detect any such support".
The Prime Minister was answering questions in Parliament after making a statement on her visit to the European Council last week.
After being asked a question by Alex Salmond, the former leader of the SNP, she pointed out that Salmond had described the 2014 independence referendum as "a once-in-a-generation vote", adding: "It seems a generation now is less than three years".