MOSCOW—The father of U.S. intelligence-leaking fugitive Edward Snowden said he intends to travel to Russia soon to visit his son even though he isn't sure they will be able to meet.

Lon Snowden has been planning a trip to Russia since his 30-year-old son was granted temporary political asylum here on Aug. 1, but the journey has repeatedly been delayed due to what he described as security concerns and a falling-out between the elder Mr. Snowden and his American legal team. He still wants to make the trip despite there being...