PRINCE SULTAN AIR BASE, Saudi Arabia—Defense Secretary Mark Esper met Tuesday with the king of Saudi Arabia during a tour of the kingdom’s military facilities as the U.S. pursues its biggest Middle East troop buildup of the Trump administration.

Mr. Esper arrived in Saudi Arabia Monday as the U.S. steps up support for Riyadh against a recent series of attacks on Saudi oil industry facilities and tankers blamed on Iran. The trip also comes amid strained U.S.-Saudi relations and growing Russian influence in the region,

Earlier this month, the U.S. military announced that it would deploy 2,000 troops, three new antimissile systems, two squadrons of jet fighters and other equipment to Saudi Arabia in an accelerating U.S. buildup meant to counter Iranian hostilities in the region.

The additional 2,000 troops are joining approximately 700 service members that had been deployed in previous rounds, including some to Prince Sultan Air Base, about 80 miles southeast of Riyadh.

The bulk of additional troops being deployed are headed to this Saudi base, Mr. Esper said Tuesday. Standing near one of the Patriot missile batteries sent by the U.S., he rejected charges that the American troops were being used as mercenaries after President Trump said that Saudi Arabia would be paying for their deployment to the kingdom. Instead, Mr. Esper said the Saudis were engaging in burden sharing.