Israel's far-right Finance Minister Bezalel Smotrich on Thursday rejected a proposal for a 21-day ceasefire in Lebanon and called for the "crushing" of the Lebanese armed group Hezbollah.

"The campaign in the north should end with a single result: crushing Hezbollah and elimination of its ability to harm the residents of the north," Smotrich said on social media platform X, adding that the ceasefire proposed by the U.S. and its allies would give Hezbollah time to "reorganize".

U.S. President Joe Biden warned Wednesday of the possibility of an "all-out war" in the Middle East as Israel put troops on alert for possible entry into Lebanon and the war in Gaza grinds on.

"An all-out war is possible," Biden told ABC chat show "The View." "What I think is, also, the opportunity is still in play to have a settlement that could fundamentally change the whole region."

The United Nations said Wednesday that some 90,000 people had been displaced in Lebanon this week, as Israel pounds what it says are Hezbollah targets across the country and the Lebanese group strikes back.

Since Monday, the U.N.'s International Organization for Migration has recorded "90,530 newly displaced persons", a statement said.

As Israeli bombs flattened buildings and sent smoke billowing skywards over Lebanon this week, Gazans looked on with both empathy and fear over how the widening war might affect them.

Israel carried out a third day of air strikes against Lebanon on Wednesday, saying it was targeting weapons caches and infrastructure belonging to Hezbollah.

The Israeli military said on Wednesday it was calling up two reserve brigades to the north, where its forces are involved in cross-border clashes with the Lebanese group Hezbollah.

"The IDF (military) is calling up two reserve brigades for operational missions in the northern arena," the military said in a statement, adding that this would "enable the continuation of combat against the Hezbollah terrorist organization".

The White House said Wednesday that a missile launched by Hezbollah in Lebanon at Tel Aviv in Israel was "deeply concerning," but that a diplomatic offramp remains to avoid "all-out war."

"It's certainly deeply concerning, obviously to the Israelis, of course, but also to us," White House National Security Council spokesman John Kirby told CNN. "There is still time and space for a diplomatic solution here to de-escalate the tensions and to prevent an all-out war."

Fadi, a type of rocket used for the first time by Hezbollah against Israel, has more explosive power and range than rockets deployed previously, but lacks precision, experts say.

Hezbollah said Tuesday that it targeted a military base in north Israel near Safed twice with salvos of rockets, as Israel pounded Lebanon with air strikes, saying it was targeting the Iran-backed group.

"In defense of Lebanon and its people", Hezbollah targeted "the Dado base" near north Israel's Safed -- the headquarters of the Israeli military's northern command -- with a total of 90 rockets, the Iran-backed group said in two separate statements.

Israel is not eager for a ground invasion of Lebanon, the country's ambassador to the U.N. Danny Danon said, as Israel carried out deadly strikes on its northern neighbor.

"We had experience in Lebanon in the past. We are not eager to start any ground invasion anywhere," Danon said Tuesday as intensified Israeli strikes stoked fears of a wider war in the Middle East.

Israel's defense minister has accused U.N. Secretary-General Antonio Guterres of failing to prevent Hezbollah attacks on Israel after the U.N. chief said Lebanon was becoming a "nightmare" like Gaza following Israeli air strikes.

"Mr Secretary General, the nightmare you speak of, is in fact a reality," Yoav Gallant said in a response to Guterres on X, adding "the reality is that Hezbollah has taken Lebanon hostage, and the U.N. is neither acknowledging their actions, nor fulfilling its fundamental obligation -- preventing Hezbollah attacks and demanding the implementation of Resolution 1701".