Theresa May used an update in the House of Commons on Brexit to accuse the Scottish National Party of constitutional game-playing" for calling a second independence Vote.
The Prime Minister told MPs the people of Scotland didn't want a second referendum.
It was the latest in a series of blows exchanged by the two leaders over Ms Sturgeon's announcement on Monday of plans for a second referendum on Scottish independence, marking a significant escalation in hostilities.
Earlier the First Minister had questioned the Prime Minister's legitimacy, telling her: "I was elected as FM on a clear manifesto commitment… The PM is not yet elected by anyone".
Ms Sturgeon said it was up to the Scottish parliament to decide when a vote would be held and warned Mrs May there should be "no blocking mechanisms".
She has called for a vote by spring 2019 on the grounds that by then voters would know what the Brexit deal was likely to bring.
However, the Prime Minister does not want to have to fight a campaign to keep the union together at a time she is carrying out negotiations with Brussels over Brexit.
She is understood to be preparing to reject demands for a vote within two years but leave the doors open for a vote after the Brexit deal is done.
The First Minister will see the approval of the Scottish Parliament for a new vote on independence next week although Mrs May would have to give approval.
The Prime Minister is expected to respond fully to Ms Sturgeon's plans once Holyrood has made its decision.