LONDON (AFP) - New Prime Minister Theresa May pledged to forge a bold, new role for Britain outside the EU and fight "burning injustice" in the country as she took office on Wednesday.

In her first remarks as prime minister, May said she wanted to build a better country that worked for all its citizens and would battle to keep the United Kingdom together.

Queen Elizabeth II invited Conservative Party leader May to form a new government in an audience at Buckingham Palace shortly after David Cameron tendered his resignation to the monarch.

Cameron decided to step down after six years as premier following the June 23 referendum on Britain's membership of the European Union, in which 17.4 million people voted to leave the bloc.

"Following the referendum, we face a time of great national change and I know because we are Great Britain, we will rise to the challenge," May said outside the prime minister's Downing Street office.

She, like Cameron, had backed Britain staying in the EU.

"As we leave the European Union, we will forge a bold, new, positive role for ourselves in the world and we will make Britain a country that works not for a privileged few but for every one of us," she said.

"That will be the mission of the government I lead and together we will build a better Britain." She also pledged to work to hold the UK together in the face of threats by Scotland's secessionist government to hold a second referendum on independence following the EU vote.

A majority in Scotland voted for Britain to remain in the EU.

"The full title of my party is the Conservative and Unionist Party, and that word unionist is very important to me," May said.

"It means we believe in the union: the precious, precious bond between England, Scotland, Wales and Northern Ireland." May, 59, is Britain's second female prime minister and the 13th of 90-year-old Queen Elizabeth's reign.

She said she wanted to create "a country that works for everyone".

"The government I lead will be driven not by the interests of the privileged few but by yours. We will do everything we can to give you more control over your lives," the former interior minister said.

May posed for photographs with her husband Philip, a senior executive at an investment fund, on the steps of 10 Downing Street, in front of the famous black door of the prime minister's office.

She was applauded by civil servants - the traditional welcome - as she stepped inside.