EDINBURGH (Reuters) - Prime Minister Theresa May does not have a mandate to take any part of Britain out of the European Union's single market, Scottish First Minister Nicola Sturgeon said on Wednesday, upping the stakes in talks for Britain to leave the bloc.

May has said Britain will be leaving the EU after 52 percent of voters backed Brexit at a June 23 referendum. While England and Wales voted to leave, the Scots and Northern Irish backed staying in the bloc, complicating divorce proceedings.

"We will seek to use whatever influence we have to shape the best, or the least bad option," Sturgeon told the Scottish parliament, providing an update on Scotland's drive to keep its EU membership.

"In my view, that does mean the UK continuing as a member of the single market. I accept that the Prime Minister has a mandate in England and Wales to leave the EU, but I do not accept that she has a mandate to take any part of the UK out of the single market."

Continuing to have access to the single market without being an EU member would mean taking part in the trade area without having a say over its rules.

Support for EU membership among Scots in the June "Brexit" referendum was 62 percent, putting Scotland at odds with much of the rest of Britain.

Sturgeon, who leads the devolved Scottish government, has raised the possibility of another independence referendum. Scots voted against secession just two years ago.

"Our guiding principle will continue to be at all times the best interests of the people of Scotland."

Sturgeon said she had held meetings with high-ranking EU officials after the June vote, including the prime minister of Malta who she said was likely to hold the EU presidency when the legal mechanism for Britain to leave the bloc is triggered.

(Reporting by Elisabeth O'Leary; Editing by Richard Balmforth)