Hezbollah has responded to far-right Israeli Minister Ben Gvir's calls for war, with the group saying it's ready.

"If 'Israel' wants to wage an all-out war, we are ready for it. Any Israeli expansion of the war on Lebanon will be met with devastation, destruction and displacement in Israel," Deputy Secretary General of Hezbollah Sheikh Naeem Qassem told Al Jazeera Tuesday.

"Our decision is not to expand the war, but we will fight it if it is imposed on us," he said.

He also claimed that President Joe Biden's cease-fire proposal is a political move ahead of the election.

"There is no serious American decision to stop the 'Israeli' war on Gaza," Qassem said.

-ABC News' Nasser Atta

Hamas will not accept a Gaza truce deal without clear commitment from Israel to a permanent cease-fire and a complete withdrawal from the Gaza Strip, Hamas official Osama Hamdan said Tuesday.

"We have communicated our position to the mediators that we cannot agree to a deal unless there is a clear position from the Israeli occupation it is committed to a permanent cease-fire and a comprehensive withdrawal from the Gaza Strip,” Hamdan said during a press conference in Beirut.

Hamdan said he does not believe Israel will commit to a cease-fire and called on Israel to submit a clear position of its readiness for a permanent cease-fire and complete withdrawal from Gaza.

"We cannot agree to a deal that does not secure, guarantee and confirm a permanent cease-fire, comprehensive withdrawal from the Gaza Strip and the completion of a serious and real exchange deal," Hamdan said.

"We asked the mediators to obtain a clear position from the Israeli occupation regarding its commitment to a permanent cease-fire and a comprehensive withdrawal," he added.

-ABC News' Ayat Al-Tawy

Hamas officials are not responding favorably to President Joe Biden's speech Friday and what they call the current proposal on the table.

A Hamas leader said no Hamas delegation has gone to Cairo, and the group is not accepting the offer given to them by mediators, the leader told Al-Mayadeen, a Lebanese news channel.

"We do not want to start from scratch, and our basic condition now is official Israeli approval of the previous paper, otherwise there will be no rounds and discussions," the leader said to Al-Mayadeen.

Separately, senior Hamas official Sami Abu Zuhri said the group frowns upon Washington and the West's calls for it to accept Biden's proposal on Gaza "as if it is Hamas who is hampering the deal," he said Tuesday.

Israel is not serious about reaching a deal in Gaza and is still maneuvering under the U.S.'s cover, Abu Zuhri said to Hamas media.

-ABC News' Nasser Atta

Qatar’s foreign ministry said on Tuesday it was "too early" to reach a cease-fire deal and that there should be a clear position from both sides on the U.S. truce proposal.

"We are waiting for a clear Israeli position that represent the entire Israeli government," Qatari foreign ministry spokesperson Majed Al-Ansari told reporters during a press briefing on Tuesday. "Any talk of reaching a deal needs a clear position from both sides towards ideas put on the table."

The deal should offer a road map for a permanent cease-fire and an end to the war, he said.

"It is too early thus far. We do not have clear positions from both sides," he said, adding that mediators remain hopeful as they push ahead with efforts to reach a deal but are "not always optimistic."

-ABC News' Ayat Al-Tawy

Israeli forces confirmed the deaths of four more hostages: Haim Peri, Yoram Metzger, Amiram Cooper and Nadav Popplewell.

IDF spokesman Daniel Hagari said the four hostages were "killed together" a "few months ago" while "IDF forces were operating" in Khan Younis in southern Gaza. Hagari said Israeli forces are "examining the circumstances" of their deaths.

Cooper, 85, was an economist and a poet, and a father of four and grandfather of 11, according to Kibbutz Nir Oz. His wife, Nurit Cooper, was also kidnapped and later released, the kibbutz said.

Metzger, 80, was a father of three and grandfather of seven. His wife, Tamar Metzger, was also abducted to Gaza and later released, the kibbutz said.

Popplewell, 51, was kidnapped with his mother, who has been released, the Hostages Families Forum said.

Peri, 80, was abducted while protecting his wife, the Hostages Families Forum said. He leaves behind his wife, five children and 13 grandchildren.

Peri's family said he "heroically survived in the Hamas tunnels, under inhumane conditions, for around 4 months," and he "survived with the hope and faith that the state of Israel will fulfill its moral duty to bring him home."

"The government of Israel and its Prime Minister have no right to leave the hostages in captivity, dismantling Israel’s foundational principle of mutual responsibility," Peri's family said. "We call upon the government of Israel to strive for an immediate deal, save those still alive, and bring those who are not, to a proper burial."

"The heartbreak that comes with this painful news should shake every citizen in the State of Israel and lead every leader to profound soul-searching," the Hostages Families Forum said in a statement Monday. "The Israeli government must send out a negotiating delegation this evening and return all 124 hostages, both living and murdered. ... We reiterate our demand to the Israeli government: approve the Netanyahu deal immediately!"