Gaza ceasefire has been overtaken by events

"We're never giving up", the US envoy added, saying more delays could mean more hostages could die and further obstacles could hamper any agreement.

Hopes that Hamas could be persuaded to accept the deal, which rose as Blinken continued his mission with visits to Egypt and Qatar, foundered after the organisation announced it had not accepted the latest US hostage-ceasefire proposal.

Key sticking points in the talks, mediated by Egypt and Qatar as well as the US, are said to include a Hamas objection to Israel maintaining its presence in the Philadelphi Corridor, a narrow 14.5 kilometre stretch of land along Gaza's southern border with Egypt.

Instead, the Hamas delegation at the Cairo talks demanded that Israel should accept the terms of the previous ceasefire deal set out on 2 July,  in accordance with a plan laid out by Washington and a United Nations Security Council resolution.

While declining the latest deal on offer, Hamas continues to maintain that it is willing to implement an agreement that serves the interests of the Palestinian people, so long as it includes a permanent ceasefire and a complete Israeli withdrawal from Gaza.

Hamas is also stipulating that any agreement should include the freedom of return for Gaza residents to their homes, relief and reconstruction, as well as a hostage-prisoner exchange deal.

Dramatic escalation

But the prospects of any meaningful progress being made in the ceasefire negotiations have subsequently been overtaken by an upsurge in violence elsewhere.

 In southern Lebanon, Israel has conducted a series of strikes against Iranian-backed Hezbollah targets. In the Israeli-occupied West Bank, the Israeli military has launched one of its largest military operations since the Second Intifada two decades ago.

Israel's justified its Sunday morning action across southern Lebanon by saying it was a pre-emptive move to thwart an imminent, large-scale rocket and drone attack from Hezbollah militants.

Israel Defence Force (IDF) officials claimed their jets had destroyed thousands of the Iran-backed armed group's rocket launchers during the attacks, in which three  militant fighters, from Hezbollah and Amal, had been killed.

Even so, Hezbollah said it had still managed to fire 320 rockets and drones at Israel. It was retaliation for the assassination of Fuad Shukr, Hezbollah's commander of operations in Beirut. The IDF said one Israeli navy soldier was killed.

Tensions between Israel and Hezbollah have increased since Israel was accused of carrying out the assassination of Hamas leader Ismail Haniyeh in Tehran last month. There are fears that the latest clashes have the potential to provoke a wider Middle East conflict. 

Top-level call for calm

In the West Bank, meanwhile, Israel has launched what it claims is a major operation against militants accused of plotting attacks against the Jewish state. The IDF has reported that nine militants have been killed, five in Jenin and Tulkarm, and four in the al-Faraa refugee camp.

The upsurge in violence in the West Bank has prompted UN Secretary-General Antonio Guterres to call on Israel to immediately halt its operation, saying it was "fuelling an already explosive situation".

He urged Israeli forces to "exercise maximum restraint and use lethal force only when it is strictly unavoidable".

At the same time, Israel has also continued to maintain its military offensive in Gaza. At least 10 people were killed on Tuesday in an Israeli airstrike on a school which was sheltering displaced families west of Gaza City. Israel claimed the school was being used as a Hamas base.

Israel's military operations in Gaza also rescued an Israeli hostage after soldiers found him in a tunnel by chance.

Qaid Farhan Al-Qadi – a Bedouin who was captured on 7 October  while working as a factory guard – was returned home on Tuesday in what the Israeli army described as a "complex operation".

The 52-year-old was located by an Israeli special forces unit called Flotilla 13 during a raid intended to capture a Hamas tunnel in southern Gaza. The IDF also recovered the bodies of six Israeli hostages seized during the 7 October  attacks during an overnight operation in Khan Younis.

The latest dramatic escalation in hostilities on several fronts certainly does not bode well for the Biden administration's hopes of implementing a ceasefire deal any time soon.

Blinken issued a warning as he ended his latest mission to the region this week, saying "time is of the essence" to secure a ceasefire deal in Gaza.  But the fact that hostilities between Israel and its various adversaries have since increased makes the prospect of any lasting ceasefire agreement even more remote.