Prime Minister David Cameron dismissed a second Scottish independence referendum as "not remotely on the cards", but he would consider nationalist demands for greater powers to be devolved from London to Scotland.

Cameron was speaking after meeting Scotland's Nicola Sturgeon in Edinburgh, the Scottish capital, just over a week after her Scottish National Party (SNP) won almost every seat in Scotland in the general election, straining Britain's unity nine months after a referendum saved it.

Scots rejected independence last year by 55-45 percent, and asked whether he would veto another such referendum.

"I think on the referendum question, it was very decisive. The Scottish people decided to stay in the United Kingdom. (Former First Minister of Scotland) Alex Salmond said at the time this was a once in a generation, potentially once in a lifetime, opportunity and I agree with that. So I don't think, as (First Minister of Scotland) Nicola Sturgeon herself has said, this is not on the cards," Cameron said.

Basking in the afterglow of her party's stunning victory last week when it won 56 of 59 Scottish seats in the United Kingdom's parliament, Sturgeon used the meeting to tell Cameron she wanted him to go well beyond an existing deal to grant more powers to the devolved Scottish government.

Although Cameron's Conservatives performed strongly in England and won an overall UK-wide majority, they won just one seat in Scotland.

Cameron had already agreed to further dismantle Britain's highly centralised system of government and to give Scotland, which already enjoys a large degree of autonomy, new tax-raising powers. But Sturgeon said she'd told Cameron she wanted him to go well beyond a deal reached last year after a process known as the Smith Commission.

Cameron said he would look at the proposals, but made no promises he would agree to them. He said he was opposed to granting Scotland full fiscal autonomy, something the SNP is pushing for.

Some accused the prime minister of stoking English nationalism ahead of the May general elections, which Cameron denied.

"I certainly didn't do that. I've always stood for the United Kingdom and for bringing our country together. I simply pointed out the danger of having an alliance between one party, the SNP that wanted to break up our country and another party, Labour, that I believe would bankrupt our party and across the United Kingdom, that was a powerful and important message," said Cameron.

"But I've always believe profoundly in the United Kingdom, and here I am in Scotland just eight days after that election delivering on the promise that I made to the Scottish people, that if I was the prime minister, the Smith Commission report on full devolution would be implemented straight away," he continued to say. "I'm the prime minister, and it will be."

The SNP argues its victory last week shows Scottish voters have decisively rejected public spending cuts imposed by Cameron's Conservatives. Sturgeon argues that any future settlement must give Scotland the power to pursue the less austere policies Scottish voters demand.

Scotland's three-centuries-old union with England could depend on the fate of another: Cameron has promised to renegotiate Britain's relationship with the European Union and hold an in-or-out EU membership referendum by the end of 2017.

Sturgeon has said that if England voted to leave the EU but Scotland voted to stay, it could trigger another referendum on Scottish independence.

The SNP is due to face Scottish voters once again in an election for the Scottish parliament next year. Some voters say Sturgeon's new mandate means she has no excuse if she fails to deliver on her promises.