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 said, referring to the procedure through which a country would withdraw from the EU.

May 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 possibilities 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."

While European leaders have urged Britain to start formal discussions over an EU exit quickly, May has said Britain would not trigger Article 50 this year, and needed a clear negotiating stance first.

BLOCKING ARTICLE 50

Scotland's position could further delay divorce talks as, under devolution rules, the parliaments of Scotland, Northern Ireland and Wales are required to consent to any EU exit, according to a report by the House of Lords.

Sturgeon said last month that Scotland's parliament would consider blocking such legislation if necessary to protect Scottish interests. She has also repeatedly warned that Scotland could split from the United Kingdom should that be the only way for it to remain in the EU.

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.

Sturgeon, who met several EU leaders in Brussels days after the referendum, said she was pleased May was willing to consider the Scottish government's options as part of the overall negotiations over the terms of Britain's exit.

But she said it would be inconceivable for a British prime minister to block a referendum if the Scottish parliament voted to hold one.

"I’ve said previously that if we want to protect our relationship with the European Union then Scotland may have to consider becoming an independent member," she said after Friday's meeting.

"If it proves not to be possible to fully protect Scotland’s interests through the UK process then the prime minister knows that a second independence referendum is of course on the table."

May said the independence issue had been settled:

"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."

Polls suggest support for independence has risen since the Brexit vote.

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 Robin Pomeroy)