Blinken met earlier in the day in Cairo with Egypt's President Abdel-Fattah El-Sisi, whose country has been helping mediate the on-off Gaza talks for months along with the United States and Qatar.
Sisi said after their meeting that it was time to put an end to the 10-month-old war in Gaza and warned of the conflict expanding in the region.
Blinken's visit to the region also included meetings in Israel on Monday.
He said Israeli Prime Minister Benjamin Netanyahu had accepted a US "bridging proposal" aimed at narrowing the gaps between the two sides after talks last week paused without a breakthrough, and urged Hamas to accept it too.
A senior US administration official told reporters travelling with Blinken that the United States expects the ceasefire talks to continue this week.
The Palestinian militant group has not explicitly rejected the proposal.
But Hamas said it overturns what was previously agreed, without specifying how, and accused Israel and its US ally of spinning out negotiations in bad faith.
"…we would very much have liked to bring [the hostages] back alive, but even bringing a body for burial in Israel is a very, very important task."— Israel Defense Forces (@IDF) Remarks regarding the 6 bodies that were rescued by The Chief of the General Staff, LTG Herzi Halevi. pic.twitter.com/2w1uWQdinNAugust 20, 2024
At stake is the fate of the tiny crowded Gaza Strip, where Israel's military campaign has killed more than 40,000 people since October according to Palestinian health authorities, and of the remaining hostages being held there.
The war in Gaza began on October 7, 2023 when Hamas gunmen stormed into Israeli communities, killing about 1200 people and abducting about 250 hostages, according to Israeli tallies.
On Tuesday, Israel's military said it had recovered the bodies of six hostages from southern Gaza.
According to Israeli authorities, 109 hostages now remain in the Palestinian territory, of whom around a third are believed to be dead.
In Gaza, Israeli forces battled Hamas-led militants in central and southern areas, and Palestinian health authorities said at least 39 people had been killed on Tuesday in Israeli strikes, including on a school housing displaced people.
Israel's military said it had struck Hamas militants embedded in the school.
Gaza's Hamas-run health ministry said on Tuesday it was still waiting for polio vaccines to arrive after the disease was discovered in the territory, where most people now live in tents or shelters without proper sanitation.
It echoed a call by the United Nations last week for a ceasefire to allow the vaccination campaign.
Blinken has called the latest push for a deal "probably the best, possibly the last opportunity" and said his meeting with Netanyahu was constructive.
He also said it was incumbent on Hamas to accept the bridging proposal.
Officials from the US, Hamas, Israel, Egypt or Qatar have not spelled out what is in the proposal or how it differs from previous versions.
Hamas rejected US comments that it was backing away from a deal, saying Egyptian and Qatari mediators knew it had dealt positively towards the negotiations and that it was Netanyahu who had obstructed an agreement with new demands.
It said it was still committed to terms it agreed with mediators in July based on a proposal made by the US in May.
Netanyahu denies obstructing a deal.
Months of on-off talks have circled the same issues, with Israel saying the war can only end with the destruction of Hamas as a military and political force and Hamas saying it will only accept a permanent, not temporary, ceasefire.
There are disagreements over Israel's continued military presence in Gaza, particularly along the border with Egypt, the free movement of Palestinians inside the territory and the identity and number of Palestinian prisoners to be freed in a swap.
Egypt is particularly focused on a security mechanism for the Philadelphi Corridor, the narrow border strip between Egypt and Gaza that Israeli forces seized in May.
Both Hamas and Egypt are opposed to Israel keeping troops there but Netanyahu has insisted they are needed to stop weapons being smuggled into the Gaza Strip.
A senior US official disputed an Axios report that quoted Netanyahu as saying he may have convinced Blinken on the point.
Egyptian security sources said the US has proposed an international presence in the area, a suggestion the sources said could be acceptable to Egypt if it was limited to a maximum of six months.
