The White House is considering options for leaving about 500 U.S. troops in northeast Syria and for sending dozens of battle tanks and other equipment, officials said Thursday, the latest in an array of scenarios following President Trump’s decision this month to remove all troops there.

The options, presented by military officials, would represent a reversal from the American withdrawal Mr. Trump wanted. It also would modify U.S. objectives—from countering Islamic State extremists to also safeguarding oil fields in eastern Syria with additional troops and new military capability.

Washington sees the fields as potential leverage in future negotiations over Syria.

“We will NEVER let a reconstituted ISIS have those fields!” Mr. Trump said Thursday in a Twitter message, referring to Islamic State.