MANILA—Asia-Pacific leaders called for greater cooperation to thwart global terrorism at a summit here on Thursday, but were silent on territorial disputes in the South China Sea that have fueled tensions in the region.

The 21 leaders gathered for the Asia-Pacific Economic Cooperation meeting, including U.S. President Barack Obama and Chinese President Xi Jinping, jointly stressed “the urgent need for increased international cooperation and solidarity in the fight against terrorism” in light of recent atrocities in Egypt...