Benjamin Netanyahu has hinted amid talks between his aide and the Qatari prime minister that negotiations are underway to recover hostages held by Hamas.
The Israeli prime minister said in a Saturday news conference that Israel's offensive in Gaza helped clinch a partial hostage-release deal in November.
This weekend his chief of Mossad intelligence met Mohamed Al Thani, the prime minister of Qatar, a country mediating with Hamas.
“The instruction I am giving the negotiating team is predicated on this pressure, without which we have nothing,” Mr Netanyahu said.
Earlier on Saturday, David Cameron had called for a “sustainable” ceasefire in the escalating Gaza conflict, as he warned that "too many civilians have been killed" by Israel.
The intervention by the Foreign Secretary, made in the Sunday Times in a joint article with the German Foreign Affairs minister Annalena Baerbock, comes amid growing pressure on Israel over its conduct of the fight against Hamas.
The two senior politicians say that neither the UK nor Germany is calling for an immediate ceasefire, but the call for a “sustainable” ceasing of conflict is a significant shift in language by the UK Government.
They wrote: “Our goal cannot simply be an end to fighting today. It must be peace lasting for days, years, generations. We therefore support a ceasefire, but only if it is sustainable.
“We know many in the region and beyond have been calling for an immediate ceasefire. We recognise what motivates these heartfelt calls.
“It is an understandable reaction to such intense suffering, and we share the view that this conflict cannot drag on and on. That is why we supported the recent humanitarian pauses.”
In recent days, the US has also expressed unease over Israel's failure to reduce civilian casualties and its plans for the future of Gaza.
Earlier on Saturday, it was reported that three hostages who escaped from Hamas clutches only to be mistakenly shot dead by Israeli troops had been carrying a makeshift white flag, according to a preliminary investigation.
Meanwhile, Liberal Democrat MP Layla Moran has said her relatives are days away from dying as they remain among the hundreds of civilians trapped in a Catholic Church without water or food.
