But one top Hamas official dismissed optimism over any potential deal as "an illusion".
Making his ninth trip to the Middle East since the war broke out last October, Mr Blinken was set to meet Prime Minister Benjamin Netanyahu.
Truce talks are due to resume in Cairo in the coming days.
In Gaza, a mother and her six children, including quintuplets, were among 28 Palestinians killed in Israeli air strikes yesterday.
The bombardment struck a home in the central town of Deir al-Balah.
Mohammed Awad Khatab, the children's grandfather, said his school-teacher daughter was with her husband and youngsters when their house was hit.
Security
The youngest child was 18 months.
The others were 10-year-old quintuplets, said Al-Aqsa Martyrs Hospital.
"The six children have become body parts. They were placed in a single bag," the grandfather said. "What did they do? Did they kill any Jews? Will this provide security to Israel?"
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