WASHINGTON — In a potential major shift in policy, U.S. military commanders want to keep at least a few thousand American troops in Afghanistan beyond 2016, citing a fragile security situation highlighted by the Taliban’s capture of the northern city of Kunduz this week as well as recent militant inroads in the south.

Keeping any substantial number of troops in Afghanistan beyond next year would mark a sharp departure from President Barack Obama’s existing plan, which would leave only an embassy-based security cooperation presence of about 1,000 military personnel by the end of next year. Obama has made it a centerpiece of his second-term foreign policy message that he would end the U.S. war in Afghanistan and get American troops out by the time he left office in January 2017.

About 9,800 U.S. troops are in Afghanistan. But the top U.S. commander in Afghanistan, Army Gen. John F. Campbell, has given the administration several options for gradually reducing that number over the next 15-months. The options all call for keeping a higher-than-planned troop presence based on his judgment of what it would take to sustain the Afghan army and minimize the chances of losing more ground gained over more than a decade of costly U.S. combat.

The timing of a new decision on U.S. troop levels is unclear. Campbell is scheduled to testify to Congress next week on the security situation, including the effectiveness of Afghan security forces after a tough summer of fighting.

Meanwhile, the U.S. military said it conducted two more airstrikes overnight on Taliban positions around Kunduz. A U.S. Army spokesman, Col. Brian Tribus, said coalition advisers were at the scene Wednesday, “in the Kunduz area advising Afghan security forces.”