MANILA—Manila was placed on its highest terror alert for the first time in 16 years, after Philippine police arrested two alleged members of an Islamic extremist terror group over a makeshift bomb planted near the U.S. Embassy Monday.

The security alert had been raised to Level 3, Philippine National Police Director General Ronald dela Rosa told a news conference Thursday, adding that checkpoints and security around public places such as shopping malls would be increased. He predicted more police raids in pursuit of terror...