NATO allies on Tuesday welcomed President Donald Trump's decision to commit more forces to Afghanistan, as part of a new U.S. strategy he said would require more troops and funding from America's partners.

Having run for the White House last year on a pledge to withdraw swiftly from Afghanistan, Trump reversed course on Monday and promised a stepped-up military campaign against Taliban insurgents, saying: "Our troops will fight to win".

U.S. officials said he had signed off on plans to send about 4,000 more U.S. troops to add to the roughly 8,400 now deployed in Afghanistan.

But his speech did not define benchmarks for successfully ending the war that began with the U.S.-led invasion of Afghanistan in 2001, and which he acknowledged had required an "extraordinary sacrifice of blood and treasure."

"We will ask our NATO allies and global partners to support our new strategy, with additional troops and funding increases in line with our own. We are confident they will," Trump said.

That comment signalled he would further increase pressure on U.S. partners who have already been jolted by his repeated demands to step up their contributions to NATO and his description of the alliance as "obsolete" - even though, since taking office, he has said this is no longer the case.

NATO Secretary General Jens Stoltenberg said in a statement:

"NATO remains fully committed to Afghanistan and I am looking forward to discussing the way ahead with (Defense) Secretary (James) Mattis and our Allies and international partners."

NATO has 12,000 troops in Afghanistan, and 15 countries have pledged more, Stoltenberg said.

Britain, a leading NATO member, called the U.S. commitment "very welcome".

"In my call with Secretary Mattis yesterday we agreed that despite the challenges, we have to stay the course in Afghanistan to help build up its fragile democracy and reduce the terrorist threat to the West," Defense Secretary Michael Fallon said.

Germany, which has borne the brunt of Trump's criticism over the scale of its defense spending, also welcomed the new U.S. plan.

"Our continued commitment is necessary on the path to stabilizing the country," a government spokeswoman said.

In June, European allies had already pledged more troops but had not given details on numbers, waiting for the Trump administration to outline its strategy for the region.

Nearly 16 years after the U.S.-led invasion - a response to the Sept. 11 attacks which were planned by al-Qaida leader Osama bin Laden from Afghanistan - the country is still struggling with weak central government and a Taliban insurgency.

Trump said he shared the frustration of the American people who were "weary of war without victory", but a hasty withdrawal would create a vacuum for groups like Islamic State and al-Qaida to fill.