Cameron and Sturgeon met in Edinburgh for their first talks since Britain's national election last week, in which Sturgeon's pro-independence Scottish National Party gained unprecedented national influence.
Sturgeon called the talks "constructive," and said the two agreed that previously drawn up plans to transfer greater governing powers from London to Scotland should be implemented as soon as possible. But she said she and Cameron disagreed on whether Scotland should control all of its tax and spending policies.
Cameron has pledged to introduce legal changes that would allow the Scottish government to control some policies including the rates of income tax in Scotland and some welfare spending.
That does not go far enough for Sturgeon, however. She says Scots want to take more substantial control over their economy, including the right to decide their own minimum wage, employment laws and business taxes.
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The prime minister said he remained committed to delivering a stronger Scottish parliament, and would consider "sensible suggestions." But he also pledged to keep the four regions that make up the UK Scotland, England, Wales and Northern Ireland together in one united nation.
"I'm a great believer that in our United Kingdom we want a strong Scottish parliament. But we also want the solidarity between the different parts of the U.K. And I don't want to lose that," he said.