WASHINGTON—The Trump administration has been holding secret talks with Russia to try to set up a de-escalation zone in southwest Syria, where Syrian government forces and rebels would be separated in hopes of ending hostilities in the region, officials familiar with the talks said.

At least two meetings have taken place so far, the last of which took place about two weeks ago in Jordan, where Jordanian officials also took part. The meetings followed a visit by U.S. Secretary of State Rex Tillerson to Moscow in April. Another...