Washington's top diplomat arrived in Israel on the second leg of his Middle East tour, after meeting Egyptian President Abdel-Fattah El-Sisi and Egypt's Foreign Minister Sameh Shoukry in Cairo.
Israel is reeling from an attack Friday that killed seven civilians outside a synagogue in annexed east Jerusalem, a day after the deadliest army raid in years in the occupied West Bank claimed 10 Palestinian lives.
The ensuing violence has prompted Israel to approve a series of punitive steps against the Palestinians, ratcheting up tensions just as Blinken begins meetings with leaders later this day.
"We've seen horrific terrorist attacks in the last couple of days that we condemn and deplore," Blinken earlier told Saudi TV channel Al Arabiya.
In a press conference in Cairo on Monday, Blinken urged "all parties to calm things down and deescalate tensions" while also stressing the "importance of working for a two-state solution".
In the latest bloodshed, Israeli troops killed a Palestinian driver in the West Bank Monday, officials on both sides said, with the army claiming the car had hit a soldier's leg before speeding off.
Since the start of the year, the Israeli-Palestinian conflict has claimed the lives of 35 Palestinians both adults and children -- albeit mostly civilian some of them were alleged militants.
Over the same period six Israeli civilians, including a child, and one Ukrainian civilian have been killed. All were shot dead in the attack Friday outside the synagogue in an east Jerusalem settlement.
In retrospect, nearly 150 Palestinians were killed in Israeli raids in the West Bank and east Jerusalem last year, making it the deadliest year in those territories since 2004, according to figures from the Israeli rights group B'Tselem.
Palestinian attacks against Israelis in the same period killed 29 people.
The United States has historically taken a lead on Middle East diplomacy, and Egypt, which has relations with Israel, has long served as a mediator in the Israel-Palestinian conflict.
Blinken was due to meet Israeli Prime Minister Benjamin Netanyahu, a veteran leader who returned to power late last year at the helm of the most right-wing government in Israeli history.
The US envoy will also travel to Ramallah in the West Bank for talks with Palestinian leader Mahmud Abbas.
Abbas met with CIA chief William Burns in Ramallah late Sunday to discuss the "dangerous developments", said the official Palestinian news agency WAFA. The US embassy declined to comment to AFP.
Blinken had long planned the visit, but the trip takes on a new urgency amid the spiralling violence.
The fatal east Jerusalem shooting was preceded by the deadliest Israeli forces operation in the West Bank in years.
Ten people were killed Thursday in the densely-populated Jenin refugee camp, in a raid Israel claims targeted Islamic Jihad operatives.
The military later hit sites in the Hamas-ruled Gaza Strip in response to rocket fire from the Palestinian enclave.
Netanyahu's cabinet has vowed a tough response and moved to punish "the families of terrorists that support terrorism" with home demolitions and other measures.
The government is also planning to rescind the rights to social security benefits of attackers' relatives, and steps to make it easier for Israeli citizens to obtain permits to carry firearms.
The latest bloodshed has heightened international concern, with Pope Francis on Sunday deploring the "death spiral".
French President Emmanuel Macron urged all parties to avoid feeding a "spiral of violence" and Russia's Foreign Minister Sergei Lavrov called for "maximum responsibility" on all sides.
Blinken on Monday met El-Sisi and then Egyptian Foreign Minister Sameh Shoukry.
Blinken commended El-Sisi for "Egypt's important role in promoting stability in the region" and "discussed ongoing efforts to de-escalate tensions between Israelis and Palestinians," said the State Department.
The diplomats and intelligence services of Egypt -- a major recipient of American military aid -- are regularly called upon to intercede between Israelis and Palestinians.
Blinken's Israel visit is part of the Biden administration's efforts to engage quickly with Netanyahu, who had tense relations with the previous Democratic administration under Barack Obama.
While there, Blinken was expected to reiterate US support for a Palestinian state, a prospect few expect to advance under the new Israeli government.
The State Department said Blinken would call for the preservation of the status quo at the flashpoint Al-Aqsa mosque compound in east Jerusalem.
Israel's extreme-right national security minister, Itamar Ben-Gvir, sparked global condemnation when he visited the site earlier this month, which is administered by Jordan.
The compound is the holiest site to Jews, who refer to it as Temple Mount, and the third most sacred place in Islam.
*This story was edited by Ahram Online