BRUSSELS — US Defense Secretary Ashton Carter has told NATO allies America will take a new look at its plans to withdraw thousands of troops from Afghanistan by the end of the year, a British official says, a fresh indication that US involvement in the country is not waning in the final months of Barack Obama’s presidency.

British Defense Secretary Michael Fallon said Wednesday that ‘‘Carter told us the troop numbers and the dispositions are being looked at again.’’

The American reassurance to NATO allies comes on the heels of Obama’s decision last week to give the military wider latitude to support Afghan forces against the Taliban, in the air and on the ground.

Far from ending the two wars he inherited from the Bush administration, Obama is wrestling with an expanded set of conflicts as his presidency nears an end, from Iraq and Afghanistan to Libya and Syria. In Afghanistan, a Taliban resurgence has upset Washington’s exit strategy, which called for troop reductions from 9,800 to 5,500 by the end of 2016.

Carter told reporters Obama indicated his willingness to reexamine force levels, based on the intensified fight against the Taliban. His comments came as NATO allies agreed to extend their Afghanistan training mission and keep troops in all four sections of the country in 2017.

NATO Secretary General Jens Stoltenberg said the allies ‘‘will have what we call a flexible regional approach, meaning that we will continue to be of course in Kabul but also out in the different regions.’’

The alliance also is ‘‘now working on the final decisions for our exact force numbers into 2017. So that’s something we will decide later on this year.’’

The US plan is facing renewed scrutiny in light of the Taliban resurgence. Former US commanders have urged Obama to keep 9,800 troops in Afghanistan into 2017.

A senior NATO diplomat said officials believe NATO will get commitments for the $5 billion needed to fund the current number of security forces through 2020. Fallon said Britain will maintain funding at nearly $100 million a year through 2020.

The moves cement NATO’s commitment to the training and advising mission in Afghanistan. The United States is now free to conduct airstrikes against the Taliban when needed in critical operations, and American troops can accompany and advise Afghan conventional forces on the ground.