Blinken, on his ninth regional tour since the Israeli war on Gaza began in October, said he was back in Israel "to get this agreement to the line and ultimately over the line".
"This is a decisive moment -- probably the best, maybe the last, opportunity to get the hostages home, to get a ceasefire and to put everyone on a better path to enduring peace and security," Blinken said as he met Israeli President Isaac Herzog in Tel Aviv.
The US secretary of state later met with Israeli Prime Minister Benjamin Netanyahu in Jerusalem, and is due to travel on Tuesday to Cairo where ceasefire talks are expected to resume this week.
Israel and Hamas blamed each other for delays in reaching a truce accord, which diplomats say could help avert a wider conflagration in the Middle East.
"We're working to make sure that there is no escalation, that there are no provocations, that there are no actions that in any way could move us away from getting this deal over the line, or, for that matter, escalating the conflict to other places, and to greater intensity," Blinken said.
"It is time for it to get done. It's also time to make sure that no one takes any steps that could derail this process."
Months of on-off talks with US, Qatari and Egyptian mediators have failed to produce an agreement.
But the stakes have risen since the late July Israeli killings of Hezbollah commander Fuad Shukr and Hamas political chief Ismail Haniyeh, and as the humanitarian crisis in the besieged Gaza Strip deepened.
Ahead of talks in Qatar last week, Hamas had called on mediators, rather than holding more negotiations, to implement a framework outlined in late May by US President Joe Biden.
Biden said Sunday that a ceasefire was "still possible" and that the United States was "not giving up", in brief comments to reporters.
Trading blame
After the Qatar meeting, the United States had submitted what mediators called a "bridging proposal", which Hamas on Sunday said "responds to Netanyahu's conditions" and includes terms that the Palestinian group would not accept.
Hamas insisted on "a permanent ceasefire and a comprehensive withdrawal from the Gaza Strip", saying Netanyahu wanted to keep Israeli forces at several strategic locations.
Netanyahu was "fully responsible for thwarting the efforts of the mediators", the Palestinian movement said in a statement.
Western-ally Jordan, Israeli captives supporters protesting in Tel Aviv, and Hamas itself have called for pressure on Netanyahu in order for an agreement to be reached.
On Sunday Netanyahu reiterated that Hamas "remains obstinate" and must be pressured, a day after his office said Israeli negotiators had expressed "cautious optimism" about reaching a deal.
US, Qatari and Egyptian mediators also reported progress.
Far-right members crucial to the prime minister's governing coalition oppose any truce.
Israel's assault on Gaza has killed at least 40,139 Palestinians, mostly women and children, according to the territory's health ministry.
Out of 251 captives seized during an October Hamas offensive in Israel, 111 are still held in Gaza.
Israeli carpet bombing of the Gaza Strip has killed two dozen Israeli captives, while more than 100 were freed during a one-week truce in November.
Tel Aviv blast
The plan announced by Biden at the end of May would freeze fighting for an initial six weeks as Israeli captives are exchanged for Palestinian prisoners in Israeli jails and humanitarian aid enters Gaza.
As efforts towards a long-sought ceasefire continued, so did the violence in Gaza but also along the Israel-Lebanon border where Israeli forces and Lebanese Hezbollah have traded near-daily fire throughout the war.
Hezbollah announced on Monday two of its fighters were killed and claimed attacks on troops and military positions in northern Israel, including with drones.
The Israeli military said its forces struck Hezbollah targets in south Lebanon.
In southern Gaza, a medical source told AFP three people were killed in Abassan village and witnesses reported Israeli air strikes near the Islamic University in Khan Younis.
The military said troops were operating in southern and central Gaza, and that the air force struck over 45 targets across the territory over the past day.
A funeral was held in Khan Younis for Palestinian photojournalist Ibrahim Muhareb, who was killed by Israeli forces on Sunday, according to an AFP correspondent.
He was laid to rest with his "PRESS" vest placed over his body.
The Committee to Protect Journalists advocacy group has said more than 100 Palestinian media workers have been killed by Israeli forces during the war.
The armed wings of Hamas and Islamic Jihad, which have battled Israeli forces together in Gaza, claimed joint responsibility for a blast in Tel Aviv late Sunday which killed the bomber and wounded one person.
The groups threatened to carry out more such attacks in Israel "as long as the occupation's massacres, the displacement of civilians and the policy of assassinations continue".
*This story was edited by Ahram Online.
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