WASHINGTON—The Pentagon is considering sending additional antimissile batteries, another squadron of jet fighters and added surveillance capabilities to the Middle East to shore up the military’s regional presence in the wake of the attack last weekend on Saudi Arabia’s petroleum industry, U.S. military officials said.

The measures under consideration also include a commitment to maintaining the presence of a U.S. aircraft carrier and other warships in the Middle East for the foreseeable future, the officials said.

The...