In the 41 days since his grand-daughter Naama Levy was kidnapped by Hamas, Shaul Levy has cycled, swum and run hundreds of miles.

The 78-year old is still a practising triathlete, and in his daily 40-mile bike rides and mile-long swims, he reaches some peace of mind amid the stress.

“I exercise every morning, and afterwards I feel strong and good,” he said. “My grand-girl is also a triathlete, a strong woman, and I hope some of that energy goes to her too.”

For such a spry figure, the five-day march he is taking part in with other hostages’ families is not too hard a pull.

Covering 50 miles from Tel Aviv to Jerusalem, and stopping overnight in villages en route, the marchers are on course to be outside prime minister Benjamin Netanyahu’s house by Saturday.

The journey, though, doesn’t really finish there. While its aim is to remind Mr Netanyahu that his priority should be the 240 captives still held by Hamas, the end will only come when every single one is back safe and well.

Yet with every day, that chance diminishes, for not all are as spritely as Mr Levy.

“There are sick people among them, old people, children and people who need medications,” Mr Levy told The Telegraph yesterday, as around 100 marchers had a lunch-stop in the village of Nof Alayon.

He wore a t-shirt bearing a picture of his grand-daughter, 19, who was serving in the Israel Defense Forces (IDF). “After 41 days, it’s getting urgent.”

To the outside eye, many might wonder whether Mr Netanyahu needs any reminders.

Haunting montages of the hostages adorn every street corner in Israel, each one bearing a photo from a family album.

They show hostages graduating from college, cuddling partners, holidaying in Europe - and in the case of a two-year toddler, taking their first steps.

Yet other than four captives released by Hamas last month, there is still no firm word on a deal to free any more, let alone all of them.

On Wednesday, Israel was reported to have turned down a Qatari-brokered deal by which Hamas would release 50 hostages in exchange for a three-day ceasefire.

Israel’s official position is that it does not negotiate with terrorists, but the realities of life in the Middle East render such a lofty approach impractical.

Over the decades, it has exchanged hundreds of jailed terrorists for captured soldiers - so many, critics say, that it incentivises Hamas to take more.

Indeed, some believe that Mr Netanyahu’s unspoken priority is destroying Hamas for good, rather than saving the hostages.

Just as their loved ones were snatched from all walks of life, many taken from the kibbutzes were Left-wing campaigners, the marchers hold no single position on what should be done.

Some believe military pressure will help force Hamas into handing hostages over. Others think Mr Netanyahu should have secured the hostages’ release first, before any invasion of Gaza. Few baulk at handing over Hamas prisoners.

“We know that may have to be done, and we can deal with that problem later,” said Mr Levy. “First, though, we just have to get the hostages home - and all at once, not a few here and there in exchange for a ceasefire.”

Where many are unhappy, though, is in the failure so far of the Red Cross to get welfare visits to the hostages, especially the more vulnerable.

The UN-backed organisation has visited detainees of terror groups in the past, such as the Afghan Taliban, and has extensive contacts in Gaza, where it operates humanitarian programs.

So far, it insists Hamas has simply refused it access, despite extensive back channel talks.

However, given Israelis’ long-standing suspicion that the UN harbours institutional bias in favour of Palestinians, many hostages’ families find it hard to take the Red Cross at its word.

“I am sure they could be doing more,” said marcher Yair Mozes, 49, whose mother Margalit Moses, 77, and father Gade Moses, 79, are among those kidnapped.

“The Red Cross is still doing humanitarian work in Gaza today. They should simply say to Hamas that if they aren’t given access to the hostages, they will scale down their humanitarian operations there.”

Mr Mozes, who wears a pendant saying: “Our hearts are captured in Gaza”, said his mother, a diabetic who had just recovered from cancer, was without her regular medication. He himself, he added, was struggling physically with the stress of past weeks.

“It is hell, just hell. You don’t go to sleep properly, and the minute you wake up, you are bolt upright.

“I’m just about managing at present, but every so often, I fall apart and sleep for ten hours straight as my body can’t handle it any more.”

The families take succour from the crowds the march attracts, who line the streets and organise meal-stops and lodgings.

“There may not be much they can do, but just having them watch gives us strength,” said Mr Levy.

But despite the cheering and the gritty smiles, the sense of peril is never far away.

On Thursday, the body of kidnapped kibbutz resident Yehudit Weiss was recovered by troops in a building near Gaza’s Al Shifa hospital. And when the march began on Tuesday, Hamas announced the death of hostage Noa Marciano, 19, another abducted IDF soldier, claiming she had been killed by an Israeli airstrike in Gaza.

Her mother’s reaction spoke volumes about what families were facing, according to Mr Levy.

“She said she actually felt some relief,” he said. “She was very sad, but at least she knew the answer.”