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

A weapon used in a strike on a UNRWA school sheltering displaced people on June 6 appears to be U.S.-made, three munitions experts told ABC News.

Journalist Emad Abu Shawiesh captured video of weapons fragments at the UNRWA al Sardi school building in Nuseirat in Gaza on June 6.

The weapon fragments seen in the video are consistent with the nose section of a U.S.-made GBU-39 "Small Diameter Bomb," Trevor Ball, a former U.S. Army explosive ordinance disposal specialist, told ABC News.

The GBU-39 also appeared to have been employed in a deadly strike on May 26 in Rafah, Gaza, according to Ball and another munitions expert, who asked not to be named due to the sensitivity of the issue.

Mark Hiznay, an associate director with the Crisis, Conflict and Arms Division of Human Rights Watch, told ABC News the image shows the remnants of a GBU-39.

N.R. Jenzen-Jones, a director at the consultancy Armament Research Services, said the image was consistent with the Small Diameter Bomb series.

“Given what we know about the IDF arsenal and munitions used in previous strikes, the remnants are most likely from a GBU-39 SDB and include a portion of the nose (forward section) of the bomb,” Jenzen-Jones said, adding that other munitions could have been used in the strike, which he had not yet assessed in detail.

-ABC News Chris Looft