WILLEMSTAD, Curaçao—A court on the Dutch island of Curaçao has authorized the local subsidiary of U.S. oil giant ConocoPhillips to seize $636 million worth of assets held on the island by Petróleos de Venezuela SA.

The move comes as Houston’s Conoco seeks to recover $2 billion in a decade-old dispute over the expropriation of its Venezuelan oil projects by the nation’s socialist government, which is struggling with an economic crunch that has caused widespread shortages of food and medicine.

The...