US Secretary of State Antony Blinken said Israeli Prime Minister Benjamin Netanyahu had agreed to an American “bridge proposal” for a ceasefire agreement in the Gaza Strip.

Now it is up to Hamas to agree, Blinken added.

The two met in Tel Aviv for talks that Netanyahu described as “positive.” His office added that he reiterated his support for an American proposal to release the hostages still held by Hamas that would take into account Israel’s security needs.

Mr Blinken had previously warned that this was “perhaps the last opportunity” to reach a ceasefire agreement as the US hoped to get a deal across the finish line.

The Americans hope that this could happen perhaps as early as this time next week, but neither the Israeli leadership nor Hamas share this optimism.

Each accuses the other of stubborn cynicism and of blocking a deal.

In a speech in Tel Aviv after the talks, Blinken spoke of the “extremely urgent need” to make progress toward a ceasefire and an agreement on the release of the hostages.

“We never give up,” he added, saying further delays could mean the deaths of more hostages and further obstacles could hamper an agreement.

The US Secretary of State will now travel to Egypt and then to Qatar to try to promote progress on an agreement.

Netanyahu reportedly told Blinken that he intends to send a negotiating team to Cairo this week to begin a new round of talks with Egyptian, Qatari and US mediators.

Meanwhile, reports from Gaza speak of a deteriorating humanitarian situation in the face of ongoing Israeli military activities.

Israel said its aircraft and troops had “eliminated dozens of terrorists” over the past day and destroyed Hamas compounds and a network of tunnels where rockets and missiles were found.

Palestinian media reported that six people were killed in an Israeli airstrike near an internet access point near the southern town of Khan Younis on Monday and another four in an attack on a car in Gaza City in the north.

The Israeli military launched a campaign to destroy Hamas in the Gaza Strip in response to an unprecedented attack on southern Israel on October 7 that killed about 1,200 people and took 251 hostage.

According to the Hamas-run Health Ministry, more than 40,130 people have been killed in the Gaza Strip since then.

In November, an agreement was reached that required Hamas to release 105 hostages during a week-long ceasefire. In return, around 240 Palestinian prisoners were placed in Israeli prisons. Israel says 111 hostages are still being held, 39 of whom are believed to be dead.

Mr Blinken was in Israel on Monday for a series of talks with key Israeli leaders.

After a meeting with Defense Minister Yoav Gallant, a large crowd of protesters outside could be heard chanting: “SOS USA, hostage now!” and “Blinken, we trust you, bring them home!” Some held pictures of hostages.

There was a clear sense of urgency in Mr Blinken’s messages.

“This is a crucial moment, probably the best, perhaps the last opportunity to bring the hostages home, to achieve a ceasefire and to put everyone on a better path to lasting peace and security,” he said ahead of talks with President Isaac Herzog in Tel Aviv.

“I am here as part of an intense diplomatic effort at the direction of President Biden to get this deal passed,” he added. “It’s time for everyone to say yes and not look for excuses to say no.”

Speaking alongside him, President Herzog blamed Hamas’s “refusal to make progress toward a settlement.”

Mr Blinken then had a three-hour meeting with Mr Netanyahu in Jerusalem, which, according to his office, “was positive and took place in a good atmosphere”.

“The Prime Minister reiterated Israel’s commitment to the current American proposal to release our hostages, which takes into account Israel’s security needs, which he strongly insists on,” the brief statement added.

On Sunday, the prime minister accused Hamas of being “completely stubborn” and insisted that “pressure must be put on the group,” which is proscribed as a terrorist organization by Israel, the United States and other countries.

A Qatar-based member of Hamas’ political bureau told the BBC on Monday that they “remain interested in an agreement,” but added that they would not attend the meetings in Cairo.

“We reached an agreement (through mediators) on July 2 … and therefore we do not need a new round of negotiations or to discuss Benjamin Netanyahu’s new demands,” said Basem Naim.

“We have shown the utmost flexibility and positivity, and the other party has seen this as weakness and has responded with more force. They are not interested in a ceasefire, they are only interested in inciting the region … and pursuing their own personal political interests.”

The United States hopes that it will be able to bridge the differences over a ceasefire agreement in the coming days.

However, this deadline is not set by the parties to the conflict, but by Washington, and the Israeli prime minister and Hamas leaders do not seem to feel the same sense of urgency.

Their statements last night were very defiant, they stuck to their positions and barricaded themselves.

On Tuesday, Mr Blinken will fly from Israel to Egypt, which, along with Qatar, is an important mediator and can convey messages directly to Hamas.

The mediators announced last Friday that they had “presented a proposal that narrows the gap between the parties” and is in line with the principles set out by President Joe Biden on May 31. The proposal will proceed in three phases:

• The first would involve a “complete and comprehensive ceasefire” lasting six weeks, the withdrawal of Israeli forces from all populated areas of the Gaza Strip, and the exchange of some hostages – including women, the elderly and the sick or wounded – for Palestinian prisoners held in Israel.

• The second phase would involve the release of all other living hostages and a “permanent cessation of hostilities”.

• The third step would be the launch of a comprehensive reconstruction plan for Gaza and the return of the remains of the dead hostages.

The Americans have not given details of their bridging proposal, but significant differences are said to remain on issues such as Israel’s continued military presence in the Gaza Strip, the right of displaced Palestinians to move freely from north to south, and the number and identity of Palestinian prisoners who could be released from Israeli prisons in exchange for Israeli hostages.

Brett McGurk, one of the Biden administration’s top envoys to the region, has been working with the Egyptians in recent weeks to resolve the sticking point of the Philadelphia Corridor, a strip of land along the Gaza-Egypt border.

Netanyahu insists that Israel maintains a presence there to prevent smuggling and Hamas’s arms buildup. Hamas says this simply means a continuation of the Israeli occupation and therefore not an end to the war.