Oil prices maintained their muted reaction to mounting tensions between Iran and the West, moving modestly higher after Tehran’s announcement that it had seized a British-flagged oil tanker Friday.

West Texas Intermediate futures rose 1.1% to $56.22 a barrel on the New York Mercantile Exchange on Monday. Brent crude, the global benchmark, gained 1.3% to close at $63.26 a barrel on London’s ICE Futures exchange.

Iranian...