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

President Joe Biden outlined Israel’s cease-fire proposal accurately in his Friday speech, the White House maintained Monday, pushing back on suggestions he miscommunicated the offer.

"The Israeli foreign minister himself acknowledged that this was the Israeli proposal ... and we're confident that it accurately reflects that proposal, a proposal that we worked with the Israelis on," White House national security communications adviser John Kirby told reporters.

Kirby also argued that Biden "felt it was important" to reveal details from ongoing cease-fire negotiations for the first time, saying it was meant to apply pressure on Hamas, not to corner Israeli Prime Minister Benjamin Netanyahu.

"We don't typically go through the details of these kinds of proposals," Kirby said. "But in this case, given where we are, given how much longer the hostages have now been held, given the fact that Hamas has reneged on several past occasions, on proposals that were sent to them, and given the fact that the Israelis really did work hard to come up with this proposal, and did so in good faith, the president felt it was important for the first time to publicly lay that out."

"This wasn't about jamming the prime minister or the war cabinet," Kirby added. "This was about laying bare for the public to see how well and how faithfully and how assertively the Israelis came up with a new proposal, how it shows how much they really want to get this done."

Kirby said Biden delivered the speech on Friday afternoon because the deal was presented to Hamas the night before.

"We're awaiting an official response by them now to take the deal," Kirby said. "This gives them what they've been looking for, which is a cease-fire and over time, and through the phases, the potential withdrawal of Israeli forces from Gaza."

-ABC News’ Fritz Farrow