Israel is fighting Iran-backed Hamas in Gaza and Hezbollah in Lebanon and has vowed to retaliate against Iran for an October 1 missile attack.
In southern Lebanon, AFP correspondents reported several Israeli air strikes on the coastal city of Tyre, after the military told people to flee before it targets Hezbollah.
The warning sparked a new exodus from the once vibrant city, where AFPTV footage showed plumes of thick black smoke rising after strikes.
"The situation is very bad, we're evacuating people," said Mortada Mhanna, who heads Tyre's disaster management unit.
"You could say that the entire city of Tyre is being evacuated," said Bilal Kashmar, the unit's media officer.
Blinken's visit to the region is his 11th since the Gaza war erupted and his first since Israel-Hezbollah violence escalated to all-out war last month.
Previous US efforts to end the war and contain its regional fallout have failed.
The Gaza war began with Hamas's October 7, 2023 attack on Israel, which resulted in the deaths of 1,206 people, mostly civilians, according to an AFP tally of Israeli official figures.
Israel's retaliatory offensive has killed 42,792 people in Gaza, also mostly civilians, according to figures from the Hamas-run territory's health ministry which the UN considers reliable.
The ministry added that more than 100,000 have been wounded, which represents over four percent of Gaza's 2.4 million population.
Blinken said Israel had "achieved most of its strategic objectives" in Gaza and now needed to build on those gains.
"Now is the time to turn those successes into enduring, strategic success," Blinken said as he left Israel, after meetings with Prime Minister Benjamin Netanyahu and other top officials.
Addressing Israel's pledge to retaliate for Iran's October 1 attack, he said: "It's also very important that Israel respond in ways that do not create greater escalation."
After Israel, Blinken began a visit to Saudi Arabia, which has put on hold talks towards a normalisation deal with Israel until a Palestinian state is created.
Blinken renewed his bid to broker diplomatic ties between them, urging Israel to seize an "incredible opportunity in this region to move in a totally different direction".
Next, he is to travel to Qatar and Britain, where he will hold talks on the Gaza and Lebanon wars.
Speaking at a summit in Russia, Iran's President Masoud Pezeshkian urged members of the BRICS group of nations to help "end the war" in Gaza and Lebanon.
A Hamas official also told AFP that a delegation led by a top official in the movement arrived in Moscow on Wednesday for talks on the Gaza war and efforts to halt it.