AMNA NAWAZ: Today, Israeli Prime Minister Benjamin Netanyahu vowed to keep attacking Iran-backed Lebanese Hezbollah with -- quote -- "full force" hours after the U.S., France and Middle Eastern allies called on both sides to accept a three-week cease-fire proposal.

Nick Schifrin has been following all this and joins us now.

So, Nick, what do we know about the proposal and how has Netanyahu responded?

NICK SCHIFRIN: The proposal is for a 21-day cease-fire between Israel and Lebanese Hezbollah, what a senior administration official last night called a -- quote -- "breakthrough."

But, as you said, Netanyahu landed in New York this afternoon and said the military campaign would continue.

BENJAMIN NETANYAHU, Israeli Prime Minister (through translator): My policy, our policy is clear.

We are continuing to hit Hezbollah with full force, and we will not stop until we achieve all of our goals, first and foremost, returning the residents of the north safely to their homes.

NICK SCHIFRIN: And, indeed, today Israel struck Beirut and said it killed the head of Hezbollah's drone unit.

Israel also released video of troops practicing for an invasion of Lebanon.

Now, we asked John Kirby, the National Security Council spokesman, whether Netanyahu has backtracked from his support, and he reiterated that Israel -- quote -- "was fully informed and aware" of every word of the cease-fire proposal before they released it and the U.S. would not have released it unless they understood that Israel supported it.

So Kirby did not say whether Netanyahu had backtracked, but we obviously have a very different public and private message from Netanyahu, and that is nothing new for Netanyahu, says Dan Byman of the Center for Strategic and International Studies.

DANIEL BYMAN, Georgetown University: Netanyahu has history of trying to play both sides on this, where he will at times appear to make concessions to U.S. officials, but then backtrack in the face of domestic politics.

Some of what the U.S. is looking for was relatively vague.

Would people agree in principle to X?

But it requires both sides to make concessions.

And Netanyahu may be reluctant to publicly agree to anything until he knows significant Hezbollah concessions are in the bag.

NICK SCHIFRIN: And, Amna, it's just not clear whether Hezbollah is willing to make the concession the U.S. is demanding, U.S. and Israel moving back from the Israeli border.

AMNA NAWAZ: Nick, what should we understand about Netanyahu's position here?

What kind of pressures is he under?

NICK SCHIFRIN: Intense pressures both from the politicians and the public.

After this hit, the Israeli media overnight members of Netanyahu's right-wing coalition said that they would bring down the government if he agreed to this cease-fire.

But we also heard politicians from the left also say that they opposed it.

We have also heard from residents who have been displaced from Northern Israel since October the 8th, when Hezbollah opened fire.

And they said that Netanyahu wasn't doing enough and they are actually -- or some of them, many of them are actually in favor of some kind of invasion.

So this tough talk from Netanyahu is popular, even if at the same time Netanyahu is very vulnerable, says Natan Sachs of the Brookings Institution.

NATAN SACHS, Brookings Institution: Netanyahu right now, although he sounds very robust, is a very weak leader.

He's very weak vis-a-vis his own coalition.

He's also very weak compared -- with regard to his own public.

There's a very large part of the public that does not believe Netanyahu and is concerned -- even when it supports this campaign in the north, is always concerned that Netanyahu has ulterior motives.

NICK SCHIFRIN: And so all eyes are on Netanyahu tomorrow, when he will speak to the U.N. General Assembly.

AMNA NAWAZ: What about on the other side of this potential cease-fire proposal?

What kind of pressures are the Hezbollah leaders under?

NICK SCHIFRIN: Israel embarrassed the group with its pager attacks and has decimated its military leadership.

So Hezbollah feels like it has to respond in order, in part to try and avoid some kind of invasion by Israeli forces.

But it's also under pressure from Lebanese to avoid a war that would destroy much of this southern part of the country.

That is a war that Iran also wants Hezbollah to avoid, says Firas Maksad of the Middle East Institute.

FIRAS MAKSAD, Middle East Institute: On one hand, it feels there is a need to escalate, if only to establish or reestablish deterrence vis-a-vis Israel.

However, it also has to take into consideration the fact that Iran right now, its primary sponsor and backer, is not itching to broaden this war.

Iran very much sees Hezbollah as a first line of defense, should Israel decide to strike at its nuclear facilities, its nuclear program.

NICK SCHIFRIN: U.S. officials know that every day that passes there could be an incident that could lead either side to escalate.

And so that's why, Amna, tonight, they are continuing to press for this 21-day cease-fire, regardless of what Netanyahu said in public today.

AMNA NAWAZ: Nick Schifrin, thank you, as always, for your reporting.

NICK SCHIFRIN: Thank you.