RANCHO MIRAGE, Calif. — President Barack Obama and leaders of Southeast Asian nations are wrapping up a two-day summit conceived to show U.S. seriousness about staying engaged and keeping a high profile in a region where a rising China has rattled American allies.

Obama and the leaders of the Association of Southeast Asian Nations will spend Tuesday discussing regional security issues. They include counterterrorism and China’s bold territorial claims to disputed waters of the South China Sea, moves that have sounded international alarms and heightened tensions with some association members.

The U.S. maintains these disputes should be resolved peacefully according to international law, a stance Obama emphasized Monday in welcoming leaders of ASEAN’s 10-nation bloc: Indonesia, Malaysia, the Philippines, Singapore, Thailand, Brunei, Vietnam, Laos, Myanmar and Cambodia.

“Here at this summit, we can advance our shared vision of a regional order where international rules and norms, including freedom of navigation, are upheld and where disputes are resolved through peaceful, legal means,” Obama said, opening the first ASEAN-only summit held in the U.S.

Obama was closing the summit with a news conference before returning to Washington.