President Donald Trump’s top national-security advisers are searching for a way to overcome the commander-in-chief’s reluctance to send thousands more troops to Afghanistan as divisions on the National Security Council complicate strategy for the 16-year-old war, officials said.

The president’s reluctance to embrace an open-ended commitment has resurrected discussion of other options, including proposals to scale back the U.S. military presence in Afghanistan or to hire private contractors to play a bigger role. Top Trump administration officials met to discuss the options Thursday after Mr. Trump asked his team for alternatives, according to current and former Trump administration officials.