WILLIAM BRANGHAM: The memorandum signed by the U.S.

and Iran has little to do with the third combatant in this war, Israel.

Top officials there expressed dismay and even derision for the deal and, as we reported, a key part of what is not in this initial agreement, the Israeli occupation of Southern Lebanon.

There, Israel continues to fight Hezbollah, the Iranian-backed militant group, despite a cease-fire that neither side is honoring.

Now Israelis say they are caught in the middle between a bad deal and constant fighting.

Here's Stephanie Sy.

STEPHANIE SY: The distant shrieks in the sky from incoming rockets, the air raid sirens, the trudge to below-ground shelters becoming almost mundane in Northern Israel.

Israel says nearly 30 of its soldiers and four civilians have died in fighting with Hezbollah.

Across the border in Lebanon, nearly 4,000 have been killed.

The cycle of violence has become all too familiar, and it's unclear whether the framework agreement for peace struck over the weekend between the U.S.

and Iran will end it.

YAEL ALON, Israeli Citizen: I'm not very happy about it.

I think it will last maybe two years until Trump is ending his term, and then we will go back to the same thing.

STEPHANIE SY: The exact terms of President Trump's deal weren't public before many Israelis had already formed their opinions.

The agreement doesn't resolve many Israeli concerns about Iran's nuclear and missile programs.

GUY BAR NATAN, Israeli Citizen: It's only American interests here, and it's in -- for the matter of national security of Israel, this is the worst, worst agreement that could ever be done.

CARMIEL FRUTKOFF, Jerusalem Resident: I don't think the agreement is a good agreement, and I think that trying to sign these kind of agreements with the bully of the neighborhood is not going to bring us long-lasting peace.

STEPHANIE SY: Top Israeli officials also made their opinions known.

BENJAMIN NETANYAHU, Israeli Prime Minister (through translator): Regarding Lebanon, we have created a buffer zone, and we will remain there as long as necessary.

Iran wanted us to withdraw from there, but that did not happen.

Do you know why it didn't happen?

Because I stood very, very firm.

STEPHANIE SY: Defense Minister Israel Katz posting on X: "We will have the ability to act independently to prevent Iran from acquiring nuclear weapons and will not withdraw from the security zones in Lebanon."

This month, Iran launched a barrage of missiles toward Israel after the IDF attacked the suburbs of Beirut and Iran's proxy Hezbollah.

The IDF has now made its deepest incursion into Lebanon in decades, destroying broad sections of the south and displacing more than a million people.

EYLON LEVY, Former Israeli Government Spokesman: There is still fighting with Hezbollah, still fighting with Iran.

Hamas still hasn't gone away.

STEPHANIE SY: Eylon Levy is a former spokesperson for Israeli Prime Minister Benjamin Netanyahu's government.

EYLON LEVY: The ballistic missile threat, the nuclear threat are a shadow of what they were in the past.

But it's like taking a round of antibiotics and finishing before the end.

The Iranian regime is still on its feet, nursing its wounds, vowing revenge, and remains dangerous.

STEPHANIE SY: He says Netanyahu is trying to salvage his legacy.

EYLON LEVY: The prime minister promised total victory, and we're nowhere near that at the moment.

STEPHANIE SY: As the military campaign drags on, Netanyahu's support has fallen.

AVIV TATARSKY, Jerusalem Resident: We have been living for years under threats caused by the belligerence of our government.

So I hope it is a lesson also for Israeli citizens that military force mainly creates problems.

STEPHANIE SY: In the seaside town of Nahariya, just six miles from the Lebanese border, tourism has taken a hit.

It's a quiet summer, but residents are vocal and divided on how much Trump is influencing Netanyahu.

YOSI MARKO, Nahariya, Israel, Resident (through translator): Trump can say whatever he wants, don't bomb here, bomb there.

If we need to carry out strikes, we will carry out strikes anywhere in the world.

YONATAN AZOULAY, Nahariya, Israel, Resident (through translator):I felt like it's the same game that's always being played.

They start, they continue, then they stop.

Daddy Trump says stop, so they stop.

Daddy Trump says continue, so they continue.

And we have a yes-man, Netanyahu, who does what he's told, and we are learning to live with that.

STEPHANIE SY: But many Israelis support military action against Hezbollah and Iran, even while questioning Netanyahu's ability to secure Israel.

In a poll earlier this month, 61 percent of Israelis said Netanyahu should not run in the next round of national elections slated for early fall.

But the prime minister announced today that he would.

While Netanyahu prepares for another election cycle, Israelis prepare for another cycle of insecurity that Eylon Levy says is unacceptable.

EYLON LEVY: That's why it is critical not to accept a new normal in which the Iranian regime thinks it can call the shots.

STEPHANIE SY: For the "PBS News Hour," I'm Stephanie Sy.