In her first U.N. speech as United Kingdom leader, Prime Minister Theresa May tried to portray an outward-facing, reliable Britain capable of delivering solutions to global challenges despite its Brexit woes, and decried violence in Syria that has affected millions of lives.

Addressing world leaders at the U.N. General Assembly on Tuesday, May pledged that "the U.K. will be a confident, strong and dependable partner internationally — true to the universal values we share together."

She gave assurances that Britain will remain "a steadfast, permanent member of the Security Council," continue meeting its NATO commitments, deploy more peacekeepers to Somalia and South Sudan, and seek to resolve conflicts across the world.

"When the British people voted to leave the EU, they did not vote to turn inwards or walk away from any of our partners in the world," she stressed, referring to Britain's June 23 referendum that approved exiting the European Union.

Saying that "no country is untouched by the threat of global terrorism," and that extremists can "transmit their poisonous ideologies directly into the bedrooms of people vulnerable to radicalization," May urged the leaders to root out "the whole spectrum of extremism — violent extremism and non-violent extremism; Islamist and neo-Nazi — hate and fear in all their forms."

The British leader also slammed the "appalling slaughter" in Syria, urging world leaders to step up efforts to bring peace to the country and to forge "a bold, new unilateralism."