Theresa May and Nicola Sturgeon held talks for about an hour during the prime minister's trip to Scotland.
Ms Sturgeon said the talks were cordial but she was "frustrated by a process that appears not to be listening".
The prime minister had earlier repeated her opposition to an independence referendum during the Brexit process.
The Scottish Parliament is expected to back Ms Sturgeon's call for a referendum on Tuesday.
The first minister says a fresh vote is needed ahead of Brexit to allow the people of Scotland to choose which path to follow.
Mrs May has repeatedly said that "now is not the time" for an independence referendum, but has not ruled out one being held after the Brexit process is complete.
Ahead of the meeting, the prime minister said leaving the European Union would be an opportunity to strengthen the ties between the nations of the United Kingdom.
Ms Sturgeon later told BBC Scotland that she had wished the prime minister well for the forthcoming negotiations with the EU, which she said the Scottish government wanted to play a constructive part in.
But she said she had been frustrated that Mrs May had not made any concessions over the first minister's demands for a distinctive Brexit deal for Scotland.
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