In her first trip as UK's Prime Minister, Theresa May has left for Edinburgh to hold talks with Scotland's Nicola Sturgeon on the United Kingdom's vote to leave the European Union.

"This visit to Scotland is my first as prime minister, and I'm coming here to show my commitment to preserving this special union," May said in a statement.

"And I want to say something else to the people of Scotland too: the government I lead will always be on your side," she said.

Sturgeon, who heads Scotland's pro-independence government, said that a second independence referendum from the UK is very likely after Scotland overwhelmingly voted to remain in the European Union during the June 23 referendum.

The United Kingdom as a whole voted 52 - 48 percent to leave the bloc, while 62 percent of Scottish voters opted to stay in the EU.

"Brexit doesn't mean Brexit for Scotland because Scotland didn't vote for Brexit," Sturgeon repeated when May took office.

Speaking to STV on Thursday ahead of the meeting, Sturgeon said she respected how other nations in the UK voted and hoped that May will respect how Scotland voted.

"My job is to seek to protect Scotland's interests," she told STV, adding that she was open to negotiating the EU exit through the UK process.

"If I'm going to be able to do that then she has to make the process open and flexible."

Despite calls for a new independence referendum, Britain's minister for Scotland said he thought the Scottish people did not want "the toxic and divisive" issue to be introduced while exiting the EU.

"Of course, there could be another independence referendum, but the big issue is: should there be another independence referendum?" Mundell told BBC radio.

"I'm clear there shouldn't and will continue to passionately make the case for that and also for the benefit Scotland gets from the United Kingdom," Mundell said.

Scotland rejected independence in 2014 with 55 percent voting to stay in the UK.

rs/jil (AP, dpa, Reuters)