The US secretary of state hopes Hamas will accept what he has called Israel's "extraordinarily generous" offer for a Gaza truce and hostage release deal.
Antony Blinken was speaking as a Hamas delegation discussed the new proposal with mediators from Egypt and Qatar.
A source close to the talks told the BBC they were cautiously optimistic.
It reportedly also involves new wording on restoring calm meant to satisfy Hamas's demand for a permanent ceasefire.
The Hamas delegation has now left Cairo and will return with a written response to the proposal, Egypt's state-affiliated Al Qahera TV said.
The Israeli government is coming under growing pressure from its global allies and the families of the hostages to agree a deal.
Israel launched a military campaign to destroy Hamas in response to the group's cross-border attack on southern Israel on 7 October, during which about 1,200 people were killed and 253 others were taken hostage.
More than 34,480 people have been killed in Gaza since then, according to the territory's Hamas-run health ministry.
A deal agreed in November saw Hamas release 105 of the hostages in return for a week-long ceasefire and some 240 Palestinian prisoners in Israeli jails.
Mediators from Egypt, Qatar and the US have been attempting for weeks to broker a new agreement that would secure another pause in the fighting and the release of the 133 hostages who Israel says are still being held, at least 30 of whom are presumed dead.
Earlier this month, Hamas rejected an Israeli proposal for a six-week truce and the release of 40 women, children and elderly or sick hostages in exchange for hundreds of Palestinian prisoners.
Hamas said it was sticking to its demands for a permanent ceasefire that would lead to a full withdrawal of Israeli troops from Gaza and the return of displaced Palestinians to their homes.
The source close to the talks in Cairo told the BBC that the new proposal from Israel was significantly different from previous offers.
On Saturday, the Axios news website cited Israeli officials as saying the proposal included a willingness for the return of people to northern Gaza and the withdrawal of Israeli troops from the east-west corridor that divides the territory and prevents freedom of movement.
It also included a willingness to "discuss the establishment of a sustainable ceasefire as part of the implementation of the second phase of the deal", the officials said.
Israeli officials and a diplomat meanwhile told the New York Times and Financial Times on Monday that Israel was also prepared to reduce the number of hostages released during the first phase to 33, down from 40.
Hamas has only said publicly that it is studying the new Israeli proposal, but an unnamed senior official told AFP news agency on Sunday that "the atmosphere is positive unless there are new Israeli obstacles".
"There are no major issues in the observations and inquiries submitted by Hamas regarding the contents [of the proposal]," they added.
FULL ARTICLE AND MORE UPDATES AT: https://www.bbc.co.uk/news/world-middle-east-68920131
