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

In a joint statement shared by the U.S. State Department on Saturday, mediators from the U.S., Egypt and Qatar said they’re working to secure a cease-fire in Gaza and the release of the hostages, and urged Hamas and Israel "to finalize the agreement" that President Joe Biden outlined on Friday.

"These principles brought the demands of all parties together in a deal that serves multiple interests and will bring immediate relief both to the long-suffering people of Gaza as well as the long-suffering hostages and their families," the statement said. "This deal offers a roadmap for a permanent ceasefire and ending the crisis."