PA via AP, Jane Barlow
Britain's Prime Minister David Cameron, left, smiles during a meeting with Scottish First Minister Nicola Sturgeon, right, at Bute House in Edinburgh, Scotland, Friday, May 15, 2015. In their first talks since Britain's national election, Prime Minister David Cameron is meeting Nicola Sturgeon, Scotland's first minister, who as the leader of the Scottish National Party engineered a stunning victory in last week's vote. Cameron, who arrived in Edinburgh on Friday, is expected to talk with Sturgeon about transferring greater governing powers from London to Scotland.

LONDON — British Prime Minister David Cameron said Friday he would consider handing more power to Scotland, but stopped short of agreeing to demands from Scotland's first minister Nicola Sturgeon to grant the territory full fiscal autonomy.

Cameron and Sturgeon met in Edinburgh for their first talks since Britain's national election last week, which saw Sturgeon's pro-independence Scottish National Party gain unprecedented national influence.

Speaking after the meeting, Sturgeon said the two agreed that previously agreed 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 get full fiscal autonomy.

Scotland has its own parliament and government, which decide policies on issues including health care, justice and education, but it must defer to the central U.K. government in London on broader issues such as defense, immigration and fiscal policies.

Cameron has pledged to introduce legal changes later this month that would allow the Scottish government to control policies including the rates of income tax and some welfare spending.

That does not go far enough for Sturgeon, who says Scots want to take more substantial control, including the right to decide their own minimum wage, employment law and business taxes.

Sturgeon's party upended Britain's political landscape last week when it swept 56 of Scotland's 59 seats in the U.K. Parliament in the general election. That surge made the SNP the third largest bloc in Parliament, a force Cameron cannot ignore.

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 parts that make up the U.K. — Scotland, England, Wales and Northern Ireland — in one united nation.

"I'm a great believer 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.

Sturgeon said Cameron had a choice to make about how he responds to the vote for her party last week.

"He can act as if it is business as usual and nothing has changed, and people will draw their own conclusions from that," she said. "They will think that Westminster isn't capable of listening or responding."