GEOFF BENNETT: There were conflicting signals today from the U.S.

and Iran over the status of negotiations to extend the cease-fire and begin talks on ending the war.

Meantime, the cease-fire between Israel and Hezbollah has all been but shattered, as Israel presses deep into Lebanon.

That spiraling situation is where Ali Rogin begins our report tonight.

ALI ROGIN: Today in Beirut, another challenge to a brittle truce, chaos and confusion, as thousands flee the capital, displacing again many people who'd already fled their homes.

NAJI MUSULMANI, Displaced Lebanese (through translator): This is the third time we are displaced, moving from a place to another.

Now I'm heading to Tripoli, to the kind people of Tripoli.

ALI ROGIN: They brace for more Israeli bombing after Prime Minister Benjamin Netanyahu ordered more strikes, despite a struggling cease-fire between the two countries.

BENJAMIN NETANYAHU, Israeli Prime Minister (through translator): I have instructed the IDF to strike terrorist targets in Beirut.

There will not be a situation in which Hezbollah attacks our cities and our citizens and its terrorist headquarters in Beirut, in Dahiyeh, remains out of bounds.

ALI ROGIN: Iranian state media released this video claiming to show a ballistic missile launch stamped with a caricature of President Trump targeting a U.S.

military base in Kuwait.

(SIRENS BLARING) ALI ROGIN: In Kuwait City, air raid sirens warned of incoming Iranian drones and missiles, which U.S.

Central Command says were intercepted.

It follows a back-and-forth skirmish over the weekend along the Strait of Hormuz.

The U.S.

says Iran downed an American drone, and CENTCOM responded by targeting air defenses and a ground control facility along the coast.

Such exchanges have become increasingly common, as diplomacy between Tehran and Washington languishes.

But after weeks of attempts to get back to the bargaining table to address the closure of the Strait of Hormuz and Iran's nuclear program, today, the Islamic Republic said it suspended indirect talks between the two countries, tying the war in Iran to Israel's widening invasion of Lebanon, insisting that any peace between the U.S.

and Iran must include Lebanon.

When asked about Iran halting negotiations, President Trump told NBC -- quote -- "I think we have been talking too much, if you want to know the truth.

I think going silent would be very good, and that could be for a long time," then telling CNBC: "I really don't care.

I couldn't care less.

Frankly, I thought they started to get very boring."

But, just hours later, Trump wrote on social media -- quote -- "Talks are continuing at a rapid pace with the Islamic Republic of Iran."

For its part, Iran's Islamic Revolutionary Guard Corps warned the people of Northern Israel, as read by state media.

MAN (through translator): Given the regime's repeated violations of the cease-fire, if this threat is carried out, we warn the residents of the northern areas and military settlements in the occupied territories to leave the area if they do not want to be harmed.

ALI ROGIN: But President Trump today, after speaking with Netanyahu, claimed that "Hezbollah agreed that all shooting will stop, that Israel will not attack them and they will not attack Israel."

The heightened tensions come as Israeli troops pushed past the Litani River last week, the deepest occupation of the territory in over 25 years.

Footage released by the IDF shows infantry seizing Beaufort Castle over the weekend, a 900-year-old crusader fortress, a strategic stronghold Israel fled from in 2000, which Firas Maksad, a Middle East expert at the Eurasia Group, says Israel will not want to give up easily.

FIRAS MAKSAD, Eurasia Group: Beaufort Castle, the Crusader castle, linchpin strategic choke point in Southern Lebanon.

In the past 24 hours, Israel was again able to occupy that strategic hilltop.

ALI ROGIN: The rising violence comes as Lebanon and Israel are scheduled to meet tomorrow in D.C.

for U.S.-brokered peace talks, which Maksad said could be the breakthrough President Trump needs.

FIRAS MAKSAD: It's very clear here that President Trump has an interest in trying to avert the worst in Lebanon.

What's happening in Lebanon is not independent from what is actually happening between the U.S.

and Iran.

Trump very much stepped in, tried to get a cease-fire in Lebanon.

It would be a win for his efforts to try and continue talks with Iran.

It's also a win from Hezbollah that is weakened and very much wants a reprieve from Israeli action.

ALI ROGIN: Until a deal is agreed upon, it's the war-weary Lebanese people who are left hoping talks will bring about a lasting truce.

FIRAS MAKSAD: Even within Hezbollah's own community, much tired and fatigued by war, there is now pressure to bring diplomacy to bear and bring this conflict to a close.

ALI ROGIN: Meanwhile, in Northern Israel, smoke can be seen rising from Lebanon as both sides continue to trade cross-border blows, with a resolution to the war no closer.

For the "PBS News Hour," I'm Ali Rogin.