From CNN Senior State Department Producer Elise Labott

Washington (CNN) – Just days after taking office, Britain's new foreign secretary visited Washington on Friday, hailing the "unbreakable alliance" between the U.S. and Britain.

"The U.S. is without doubt the most important ally of the UK," William Hague said after lunch with Secretary of State Hillary Clinton. He welcomed President Barack Obama's description of the "extraordinary special relationship" between the two countries.

Hague was announced as Britain's foreign secretary this week after a coalition government was formed between Prime Minister David Cameron's Conservative Party and the Liberal Democrats.

Clinton and Hague said their talks focused on Afghanistan, Iran and the economic crisis in the euro zone.

Hague's visit comes during a week in which Afghan President Hamid Karzai and more than a dozen members of his cabinet came to Washington for three days of talks, including meetings with Clinton and Obama.

At a press conference with Hague, Clinton said they discussed the "shared mission" in Afghanistan, and Hague had reaffirmed the British government's commitment to "achieving long-term stability there."

"The U.S. is deeply appreciative of the British contribution in Afghanistan," Clinton said.

Shorty after getting the position, Hague said he would focus on Pakistan and Afghanistan and would protect Britain's "special relationship" with the United States.

Clinton said that she was "very intrigued" by the outcome of last week's election in the UK and that the Obama administration was looking forward to "working with the new British government."

"We will continue to build on the deep and abiding trust that exists between the British and American people for a very long time," Clinton said.