JERUSALEM — Amid rocket attacks by the militant group Hezbollah into Israel and Israeli bombardment around Beirut, Secretary of State Antony Blinken began a tour of the Middle East on Tuesday, making renewed calls for a cease-fire in the Gaza Strip and a diplomatic solution to the escalating conflict in Lebanon.

Meeting with Prime Minister Benjamin Netanyahu in Jerusalem, Blinken pressed Israel “to capitalize on” the killing last week of Hamas’ leader. Yahya Sinwar, and to end the war with Hamas in Gaza, a State Department spokesperson, Matthew Miller, said in a statement.

On his 11th trip to the Middle East since the conflict began a little more than a year ago, Blinken met with Netanyahu for 2-1/2 hours. His visit was bracketed by the sounds of air-raid sirens in multiple locations across Israel during the morning and afternoon as the military tracked what it called Hezbollah “projectiles” coming from Lebanon. The morning attack, on an Israeli military base near Tel Aviv, sent residents fleeing into shelters but caused no casualties or significant damage, officials said.

In Beirut, the Lebanese capital, rescue workers pulled bodies from the rubble of buildings hit overnight by the Israeli military, killing at least 18 people, including four children, according to Lebanon’s health ministry. The buildings were near Rafik Hariri University Hospital, the largest public health center in Lebanon, which was also damaged.

On Tuesday afternoon, a separate Israeli airstrike leveled a building in the Dahiya area, south of Beirut, minutes after a Hezbollah spokesperson briefed reporters nearby. The Israeli military described the target as Hezbollah intelligence headquarters, with 25 Hezbollah members present.

The spokesperson, Mohammad Afif, told reporters that Hezbollah had taken responsibility for an aerial attack that targeted Netanyahu’s house in Caesarea, in coastal Israel, on Saturday, which his office has called an assassination attempt. Israeli censors on Tuesday allowed the release of images showing drone damage to what the Israeli news media described as a bedroom window above a swimming pool.

As Blinken met with Israel’s leaders, the Israeli military confirmed it had killed Hashem Safieddine, the presumed successor to Hezbollah’s assassinated leader, Hassan Nasrallah. Speculation about Safieddine’s fate had swirled since Israeli warplanes unleashed strikes targeting a meeting of senior Hezbollah leadership around midnight on Oct. 3.

The Israeli military said it also killed Hussein Ali Hazima, head of Hezbollah’s intelligence headquarters, in the same strike.

As news broke about Safieddine’s death, a new wave of Israeli airstrikes sounded across the Lebanese capital Tuesday.

President Joe Biden and his administration have repeatedly tried to calm the widening regional conflict. In addition to fighting Hamas in Gaza and Hezbollah in Lebanon — both groups are backed by Iran — Israel is said to be weighing retaliation against Iran for an Oct. 1 missile barrage that Tehran said had been payback for the killing of Nasrallah.

Both Netanyahu and the militant groups have repeatedly rebuffed entreaties to show more restraint and reach a cease-fire.

In his meeting with Blinken, the prime minister agreed that “the elimination of Hamas leader Yahya Sinwar is likely to have a positive influence on the return of the hostages, the achieving of all the objectives of the war and the day after the war,” his office said in a statement.

But it said nothing about whether the killing created an opening for a cease-fire in the near term.

Netanyahu and Blinken, according to statements by the United States and Israel, discussed one of the biggest unanswered questions about the conflict: How will Gaza be governed after the war.

Miller said Blinken had “emphasized the need for Israel to take additional steps to increase and sustain the flow of humanitarian assistance into Gaza and ensure that assistance reaches civilians throughout Gaza.”