During President Barack Obama ’s first term, some members of his National Security Council lobbied to pull a U.S. fighter squadron out of an air base in Qatar to protest the emirate’s support of militant groups in the Mideast.

The Pentagon pushed back, according to former U.S. officials involved in the discussion, saying a regional military command the U.S. maintains at the base was vital to American operations in the region. The issue was decided in late 2013 when the U.S. extended its lease on the base and didn’t pull out any planes.

The episode, not previously reported, reflects long-standing divisions within the Obama administration over America’s widening alliance with Qatar. The problem is that the very traits making the Persian Gulf emirate a valuable ally are also a source of worry: Qatar’s relationships with Islamist groups. […]