JERUSALEM, Jan 30 (Reuters) - U.S. Secretary of State Antony Blinken urged Israelis and Palestinians to ease tensions on Monday during a visit to Jerusalem, reaffirming a long-stalled peace vision of two states side by side as the only path forward.

Arriving amid the bloodiest violence in years, Blinken focused censure on a Palestinian gun spree outside a synagogue that put Israel on high alert but also cautioned against any celebration or avenging of such bloodshed.

Seven people were shot dead in Friday's attack by an East Jerusalem man who was himself killed by police. Lionised by many fellow Palestinians, he had no known links to militant groups.

A day earlier, Israel carried out an unusually deep raid on the Jenin refugee camp in the occupied West Bank, killing 10 residents, most of them gunmen. At least 35 Palestinians, including fighters and civilians, have died in violence surging since Jan. 1, medical officials say.

"It is the responsibility of everyone to take steps to calm tensions rather than inflame them," Blinken told reporters after landing in Tel Aviv.

Friday's rampage, he said, "was more than an attack on individuals. It was also an attack on the universal act of practising one's faith. We condemn it in the strongest terms.

"And we condemn all those who celebrate these and any other acts of terrorism that take innocent lives, no matter who the victim is or what they believe. Calls for vengeance against more innocent victims are not the answer."

Israeli Prime Minister Benjamin Netanyahu, whom Blinken met later on Monday, has called for more citizens to carry guns as a precaution against such street attacks. But he has also warned Israelis not to resort to vigilante violence.

Blinken was due to see Palestinian President Mahmoud Abbas on Tuesday.

Palestinian officials said Israeli settlers had set fire on Monday to two cars near the northern West Bank city of Nablus and thrown stones at a house near Ramallah, following a similar attack on Sunday.

Elsewhere in the West Bank, Palestinian officials said Israeli troops killed a 26-year-old man at a checkpoint. The army said troops opened fire on the man's car after he rammed into one of them and tried to flee an inspection.

The last round of U.S.-sponsored talks on founding a Palestinian state alongside Israel stalled in 2014.

Netanyahu's new hardline government includes partners who oppose Palestinian statehood, and control over the Palestinian territories is divided between Abbas, who favours diplomacy, and rival Hamas Islamists, who are sworn to Israel's destruction.