Top Trump administration officials signaled the U.S. didn’t intend to assume sole responsibility for safeguarding tankers in the Persian Gulf after attacks Washington blames on Iran, because America has become less dependent on oil supplies from the region.

Air Force Gen. Paul Selva, the vice chairman of the Joint Chiefs of Staff, on Tuesday said the Trump administration wasn’t planning to replicate the mission the Reagan administration undertook in the 1980s, when the U.S. protected Kuwaiti oil tankers from Iranian attack...