Oil prices rose slightly on Monday and stocks in Asia were mostly higher as investors reacted cautiously after President Trump said the United States would help ships navigate the Strait of Hormuz.

Mr. Trump wrote on social media that, beginning Monday morning, the United States would “use best efforts” to get ships out of the strait that were not involved in the conflict. Mr. Trump offered scant details about how the process would unfold. The U.S. Central Command indicated that the American role would involve coordinating safe traffic among the stranded ships.

On Saturday, Mr. Trump had said that he was reviewing a peace proposal from Iran, but that he doubted it would be acceptable.