"No people anywhere should live with daily violence, with attacks in the streets, with knives, with scissors, cars," he said, alongside Israel's PM.
Later, Mr Kerry met the Palestinian president in the West Bank.
Nineteen Israelis and more than 90 Palestinians, many of them assailants, have been killed in weeks of unrest.
The attackers who have been killed have been shot by their victims or security forces. Other Palestinian fatalities have occurred in clashes with troops in the West Bank or in cross-border violence in Gaza.
Hamas, the Palestinian Islamist movement which runs Gaza, said it condemned Mr Kerry's remarks and considered his statement "a full support of the Israeli crimes and terrorism".
Soon after Mr Kerry spoke, a Palestinian driver rammed into Israeli security personnel at a checkpoint in the north of the occupied West Bank, injuring four people, the Israeli military said.
The driver, from the West Bank city of Jenin, was shot and wounded.
The militant Palestinian Islamic Jihad movement said the attack, near the city of Nablus, was "a heroic response to John Kerry plans to abort the intifada [Palestinian uprising]".
Mr Kerry said he would speak to Israeli Prime Minister Benjamin Netanyahu about how to "to push back against terrorism, to push back against senseless violence, and to find a way forward to restore calm and begin to provide opportunities".
It is the secretary of state's second visit to meet Israeli and Palestinian leaders since peace talks collapsed in April 2014.
He is not expected on this trip to try to bring the sides back to the negotiating table, despite the worst unrest since last summer's war between Israel and Hamas.
The surge in violence began in September this year when tensions at a flashpoint holy site in Jerusalem revered by Jews and Muslims boiled over, amid rumours that Israel planned to relax long-standing rules to strengthen Jewish rights at the complex. Israel has repeatedly denied such claims.
US Secretary of State John Kerry has denounced as "acts of terrorism" a wave of Palestinian attacks targeting Israelis, on a visit to Jerusalem.