As President Trump sent conflicting messages about whether any progress had been made on a deal to end the war with Iran, Prime Minister Benjamin Netanyahu of Israel on Monday signaled that his country’s fight with the Iranian-backed Lebanese militant group Hezbollah would intensify.

“We are at war with Hezbollah,” Mr. Netanyahu said in a video on social media.

Despite an American-brokered cease-fire that took effect in April, Israel and Hezbollah have continued to clash, with each side accusing the other of violating the truce. The fighting has recently escalated, exposing the limits of the fragile agreement.

In Mr. Netanyahu’s video statement on Monday night, he said that Israeli forces had in recent weeks killed more than 600 Hezbollah militants and indicated that the military would intensify the pressure.

“But we are not removing our foot from the pedal,” Mr. Netanyahu said. “On the contrary, I said to press on the pedal even more.”

An intensification of the fighting between Israel and Hezbollah could add yet another complication to the already complex negotiations between Iran and the United States. Iran has said that it wants Lebanon included in any agreement, while Mr. Trump has not mentioned the conflict between Israel and the Iranian proxy in his flurry of posts about a potential deal since Saturday.

The death toll from Israeli strikes on Lebanon since fighting with Hezbollah reignited in March has reached 3,185 people, Lebanon’s health ministry said on Monday, and more than 9,600 people have been wounded. The renewed fighting, which started when Hezbollah began strikes on Israel after the American-Israeli attack on Iran in late February, has displaced hundreds of thousands of people.

The Israeli military on Monday night said that it had struck more than 70 Hezbollah sites in several areas across Lebanon in the past day. In the area of Tyre, a coastal city in southern Lebanon, the military struck about 10 command centers, weapons storage facilities and other sites it said were used by Hezbollah to advance attacks against Israeli soldiers and civilians. The Israeli Air Force also “eliminated” Hezbollah militants on motorcycles in southern Lebanon in the area where Israeli soldiers are operating, the military said.

Hezbollah issued at least eight statements about attacks on Israel and Israeli soldiers in Lebanon on Monday, according to the militant group’s media arm Al Manar.

Hezbollah’s leader, Naim Qassem, in a speech to the Lebanese people on Sunday, said that he welcomed a deal between Iran and the United States and hoped that the agreement would include his group. But he rejected the direct negotiations between Israel and the Lebanese government, brokered by the United States, which have taken place since April.

While the terms of the possible agreement to cease hostilities between the United States and Iran are murky, three senior Iranian officials told The New York Times on Saturday that the agreement would halt the fighting on all fronts, including Lebanon.

How any such deal would address the fundamental issues in the conflict in Lebanon — among them the disarming of Hezbollah and the withdrawal of Israeli troops from the Lebanese border territory they now occupy — is unclear.

On Sunday, Mr. Netanyahu of Israel said that Mr. Trump had in a weekend phone call “reaffirmed Israel’s right to defend itself against threats on every front, including Lebanon.”