A prominent Lebanese politician close to Hezbollah called on President Trump on Monday to impose a new cease-fire in Lebanon, as Israel threatened fresh strikes on the outskirts of Beirut, the Lebanese capital.

The politician who has served as an emissary between Hezbollah and the United States, Nabih Berri, said in an interview with The New York Times that Hezbollah was open to a renewed cease-fire, and suggested that only the United States could press Israel to abide by one.

“No one can make a real cease-fire except for Trump,” said Mr. Berri, the speaker of the Lebanese Parliament. “This is the only way.”

Mr. Trump said on Truth Social on Monday afternoon that he had spoken with Prime Minister Benjamin Netanyahu of Israel and indirectly with Hezbollah. He said he had concluded that “Israel will not attack them, and they will not attack Israel.”

Neither side confirmed his assertion.

Mr. Berri, who leads the Amal Movement, one of the two Shiite political parties along with Hezbollah,, did not say whether he spoke to Mr. Trump after his interview with The Times. But his comments to The Times came as the already shaky truce between Hezbollah, the Iran-backed militant group and political party, and Israel teetered on the brink of complete collapse. While both Hezbollah and Israel have continued their attacks since that truce went into effect in April, over the past week the fighting has sharply escalated.

Israeli forces have pushed deeper into Lebanon, beyond the swath of land they seized and occupied earlier in the war, while Hezbollah has continued to attack Israeli troops and targets in northern Israel.

The war has killed more than 3,200 Lebanese and 30 Israelis, according to the authorities in both countries.

In a further escalation on Monday, Mr. Netanyahu said that he had ordered attacks on Beirut’s southern suburbs, a densely populated area where Hezbollah holds sway and which Israel has mostly refrained from striking since the April truce.

That message sent thousands fleeing from the suburbs into central Beirut.

Mr. Berri’s comments suggests that Hezbollah is eager to secure a new truce.

“If there is a serious cease-fire, I guarantee Hezbollah will be committed to it,” Mr. Berri said, adding that the message was coming directly from Hezbollah.

Mr. Berri declined to elaborate further on what he meant by a “serious cease-fire,” but suggested that the details of a more lasting truce — such as disarming Hezbollah and Israeli forces currently occupying Lebanese territory — could be worked out in subsequent negotiations.

The Lebanese government and Israel are set to meet on Tuesday for their next round of U.S.-mediated talks in Washington aimed at defusing the conflict.

Secretary of State Marco Rubio has presented a new de-escalation proposal to President Joseph Aoun of Lebanon and Mr. Netanyahu, a U.S. official said on Sunday. Under the plan, Hezbollah would halt attacks on Israel as a first step, after which Israel would refrain from expanding its military campaign in and around Beirut, the official said.

In recent weeks, Iran has also pushed to include an end to the fighting in Lebanon as part of a broader cease-fire deal with the United States over the American-Israeli war with Iran. But Mr. Berri suggested that Hezbollah could be open to a cease-fire that is not contingent on a wider U.S.-Iran agreement.

“A deal that is separate from Iran, or with Iran,” does not matter, he said. “We need a cease-fire. Israel wants to negotiate while it’s bombing and this is very costly for us.”

Hwaida Saad contributed reporting.