The US must launch a “Plan B” in negotiations with Israel and Hamas if the latest talks fall through this week, the families of hostages held in Gaza have said.

Joe Biden, the US president, said last week that negotiators were “closer than we’ve ever been” to securing a ceasefire deal that would release hostages held by Hamas.

It was hoped a multi-stage agreement could be finalised early this week, but the talks have floundered amid claims that the terror group is “backing off” from a compromise proposed by the US.

Three family members of Hamas hostages told The Telegraph that if the latest talks fall through, the US should abandon its negotiating strategy and launch a “Plan B” that could include an all-or-nothing deal with a shorter timeline for peace.

The latest deal involves several stages, with a limited ceasefire in the first stage and the release of some hostages. Both sides have claimed the other is holding up talks, but the US says Benjamin Netanyahu, the Israeli prime minister, has agreed to the “bridging proposal”.

Hamas in return accused Mr Netanyahu of walking back his support for the US’s plan, which could also include the withdrawal of Israel Defense Forces (IDF) troops from the Philadelphi Corridor, a buffer zone separating Gaza from Egypt.

The terror group has named Yahya Sinwar, the architect of the Oct 7 attacks, as its new political leader after the assassination of Ismail Haniyeh, the former leader, last month.

Ruby Chen, the father of a US-Israeli citizen who was killed during the attacks while serving in the IDF, said the US should change its strategy if the latest talks fall through. His son’s body is being held by Hamas in Gaza.

“If you’re trying to get an objective, and if after some point in time you see you’re not reaching that objective, you look at the game plan and see if you’re heading towards that goal,” he said.

“And if not, then there should be a Plan B. Each time that I meet a US administration official, I ask: ‘What is Plan B?’.

“God, help me, I do hope that they do have a Plan B. Maybe it is time to look at that Plan B, if we’re not able to resolve this in the next couple of days.”

The US-backed talks have focussed on a multi-stage deal, which some believe is holding up a ceasefire because neither side trusts that a truce would hold.

An alternative plan, involving all hostages released at once and a full ceasefire agreed, would be more difficult to negotiate.

However, Mr Chen’s call for a new approach was backed by Maya Roman, who is related to the Israeli hostage Carmel Gat.

She said the negotiations were at an “important crossroads” ahead of the US election.

“Because of the structure, with the stages, it kind of requires both sides to accept this kind of lack of clarity about what’s going to happen,” she said.

“So it requires a little bit of trust, which obviously does not exist. And so I do think that if this fails again, maybe we need a different strategy.

“This might be a different structure of a deal, one that is everything for everything. We can’t do the stages thing because there’s just not enough trust.”

Antony Blinken, the US secretary of state, ended his ninth visit to the Middle East since the conflict on Tuesday by warning that “time is of the essence” for a deal.

“Our message is simple. It’s clear and it’s urgent,” he told reporters before leaving Qatar. “We need to get a ceasefire and hostage agreement over the finish line, and we need to do it now.”

The talks come amid protests against US support for Israel at the Democratic National Convention in Chicago this week, where Kamala Harris will accept the party’s nomination for November’s presidential election.

Ms Harris has distanced herself from Mr Netanyahu, who is unpopular among some of her party’s voters. She did not attend his address to the US Congress last month.

Gili Roman, the brother of Hamas hostage Yarden Roman-Gat who was released in November, said he believed Ms Harris would remain committed to the talks if she wins the election, but warned the lack of trust in negotiations could sink the latest US-proposed deal.

“I think that some people in the West think of this deal as a deal between two law firms that obey the Western law,” he said.

“This is not the case. It’s against the terrorists. They’re already proven that they do not respect the terms of the deals that they’re signing.”

He said Israel would have “no leverage” if it agreed to a permanent ceasefire in stage one of the deal, adding: “We will not be able to get the rest of our people back.”

“The first and most fundamental thing that needs to happen is Hamas needs to adhere to the concept which this deal is built upon,” he said.