JERUSALEM — As Israelis and Palestinians grappled on Wednesday with the new-old reality of spiraling violence, Israeli security forces revived a controversial antiterrorism policy, demolishing the East Jerusalem home of a Palestinian man who plowed his car into pedestrians last month, killing a baby and a young woman.

Israel’s resurrection of the harsh tactic it all but abandoned a decade ago followed Tuesday’s brutal synagogue killing of four ultra-Orthodox men in midprayer, an attack that put the nation on edge. Jewish mothers publicly demanded security guards posted outside schools, the defense minister rescinded plans to relax roadblocks in the occupied West Bank, and the mayor of Ashkelon barred Arab workers from construction projects at his city’s kindergartens.

“I’m being a bit more cautious — I am not riding my bike on the main roads, in case somebody gets an idea,” Pery Harma, a father of three young children, said as he stopped with them at a juice kiosk along a West Jerusalem bicycle path. “Maybe things have to get bad before they get better. Maybe these events will remind the majority how necessary it is to reach a compromise.”

Palestinians, too, were worried, about the possibility of revenge attacks, about security forces under pressure being overzealous and about a crackdown that included new checkpoints blocking off some of their East Jerusalem neighborhoods. As sporadic clashes between youths and troops erupted, Palestinian bus drivers skipped work for the third day running to protest the death of a colleague found hanged Sunday night in what the Israeli authorities say was a suicide but his family says was a lynching.