By Russell Cheyne

EDINBURGH (Reuters) - Prime Minister Theresa May said on Friday that Britain would not trigger formal divorce talks with the European Union until a "UK approach" had been agreed, bidding to appease Scots who strongly oppose Brexit.

May made the comment after meeting First Minister Nicola Sturgeon, head of the pro-independence Scottish government which says pro-EU Scots should not be dragged out against their will and has been looking at ways to keep Scotland in the bloc.

Scotland voted by 62-38 percent to stay in the European Union in the June 23 referendum while the United Kingdom as a whole voted 52-48 percent to leave, a result which Sturgeon has said made the prospect of another vote on Scottish independence "highly likely".

"I have already said that I won't be triggering Article 50 until I think that we have a UK approach and objectives for negotiations - I think it is important that we establish that before we trigger Article 50," May told broadcasters, referring to the procedure through which a country would withdraw from the EU.

May's said her decision to visit Sturgeon on her own turf less than 48 hours after taking office underlined her determination to keep Scotland in the United Kingdom after the Brexit vote had revived the issue of independence, which Scots rejected in a 2014 referendum.

Sturgeon has said she will explore all options for keeping Scotland in the EU and May, who herself had backed the campaign to remain in the bloc, said she wanted the Scottish government to be involved in the Brexit talks.

"I will listen to any options they bring forward. I've been very clear with the first minister today that I want the Scottish government to be fully engaged in our discussions," May said. "I want to get the best possible deal for the whole of the United Kingdom."

"SCOTLAND HAS HAD ITS INDEPENDENCE VOTE"

Scots rejected independence by 55-45 percent in the referendum two years ago, but since then, Sturgeon's Scottish National Party has gone from strength to strength, winning 56 of Scotland's 59 seats in the British parliament in the 2015 election.

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"As far as I'm concerned the Scottish people had their vote, they voted in 2014 and a very clear message came through, both the United Kingdom and the Scottish government said they would abide by that," May said.

Sturgeon said on Wednesday she wanted May to enable the Scottish government to explore possibilities for Scotland to remain in the EU as a central part of the overall negotiations with the bloc over the terms of Britain's exit.

She has also repeatedly said that Scotland should be able to conduct talks directly with EU counterparts, and met several EU leaders in Brussels during a visit there days after the referendum.

If independence then turns out to be the best way for Scotland to remain an EU member, Sturgeon argues there should be another referendum on the issue. Polls suggest support for independence had risen since the Brexit vote.

On Friday, Sturgeon said it would be inconceivable for a British prime minister to block a referendum voted for by the Scottish parliament.

"I work on the basis that trying to block a referendum, if there's a clear sense that that's what people in Scotland want, would be completely the wrong thing to do," Sturgeon told Sky News after the meeting with May on Friday.

May's Conservative Party, unpopular in Scotland for decades, holds only one of Scotland's 59 seats in the Westminster parliament, although it has recently improved its standing, coming second to the SNP in the Scottish parliamentary election in May.

It is now the official opposition to the SNP in Edinburgh, having beaten the once dominant Labour Party into third place.

(Writing by Estelle Shirbon and Michael Holden, Editing by Guy Faulconbridge and Angus MacSwan)