As Palestinian militant group Hamas awaits for Israeli's formal response to its acceptance of a 60-day truce, Prime Minister Benjamin Netanyahu faces mounting pressure on all fronts to accept a deal amid growing opposition at home.

Israeli media widely reported that relatives of freed hostages briefly blocked southbound traffic on Tel Aviv's Ayalon Highway, demanding for a deal to release the remaining captives held by Hamas in Gaza and protesting Israel's plan to expand military control of Gaza City.

The demonstrators held a pink-and-purple banner reading, "Occupying Gaza would mean sacrificing the hostages and soldiers". They also chanted, "Their time is running out, a deal is on the table," and "Enough killing, enough bereavement, hostages above all," according to Walla, a Hebrew news portal.

However, far-right National Security Minister Itamar Ben Gvir rejected any partial deals, saying Netanyahu has "no mandate to go for a partial deal", and pushed Netanyahu to "go all the way" to "destroy Hamas", adding that the "blood of our soldiers is not worthless", The Times of Israel reported on Tuesday.

Israeli Finance Minister Bezalel Smotrich said Hamas eased its demands because it fears the planned Israeli offensive in Gaza City would destroy the group and said that Israel cannot surrender "and grant the enemy a lifeline".

Majed al-Ansari, the Qatari Foreign Ministry spokesperson, confirmed that his country and Egypt have received a positive response from Hamas to a ceasefire proposal that aimed at reaching a comprehensive agreement to end the war during a press conference in Doha.

Al-Ansari also said that there was no timeframe for when Israel would answer and that almost 98 percent of what had been agreed by the Israelis was included in the recent proposal.

Hamas and other Palestinian factions on Monday have announced their agreement to the Gaza ceasefire proposal presented by Egyptian and Qatari mediators.

A Hamas source revealed that Cairo and Doha will contact US Special Envoy to the Middle East Steve Witkoff to advance the negotiation process with Israel, with the aim of reaching a final agreement, Xinhua News Agency reported.

Further, the proposal reportedly stipulates a prisoner exchange deal that includes the release of 10 living Israeli hostages in exchange for the release of 140 Palestinian prisoners serving life sentences and 60 others serving sentences of more than 15 years.

Despite the latest developments, the United Nations human rights office said Israel was still not doing enough to stop widespread starvation in Gaza.

"In the past few weeks, Israeli authorities have only allowed aid to enter in quantities that remain far below what would be required to avert widespread starvation," UN spokesperson Thameen Al-Kheetan in Geneva was quoted as saying by Al Jazeera.

In a video posted on X, Younis Alkhatib, President of the Palestine Red Crescent Society (PRCS) said on World Humanitarian Day, they remind the world that Palestinian humanitarian workers "have been deliberately targeted more than anywhere else".

"No state should enjoy impunity. No state should be above the law. The international community is obliged to protect humanitarians," he said.