The Israeli defense minister said Friday that the military’s capture of a strategic ridge in Lebanon a day earlier had consolidated its foothold in the south of the country, adding to concerns that Israel intends to prolong its monthslong occupation there.

The Ali al-Taher ridge, about six miles from Lebanon’s border with Israel, sits above a sprawling underground base for Hezbollah, the Lebanese militant group that Israel has long fought.

The ridge had increasingly become a focal point of the conflict, which reignited in March after the U.S.-Israeli attack on Iran, Hezbollah’s chief backer.

The Israeli defense minister, Israel Katz, said in a video statement that the capture of Ali al-Taher marked “the completion of the process of consolidating our hold on the security zone in southern Lebanon,” referring to an Israeli-occupied strip of Lebanese territory along the border.

Hezbollah’s media office did not respond to a request for comment on Israel’s claim that it had captured the ridgeline. The office of the Lebanese presidency declined to comment.

In June, Israel and Lebanon agreed to a U.S.-brokered framework intended to end the fighting and eventually restore Lebanese control over the country’s south.

Under the plan, the Lebanese military would disarm Hezbollah and deploy in designated “pilot zones” in southern Lebanon as Israeli troops progressively withdrew. That process has largely stalled, however, with Israel and Hezbollah at odds over which side must act first. Hezbollah has consistently rejected demands to put down its weapons.

Orna Mizrahi, a former Israeli deputy national security adviser who specializes in Lebanon at the Institute for National Security Studies in Tel Aviv, said that, in Israel’s view, the pilot zone experiment had failed because Lebanon was not doing enough to prevent Hezbollah from returning to areas vacated by Israeli troops. “The big question is what’s next,” she said.

Lebanese officials, for their part, have said that continued Israeli attacks and the lack of further military withdrawals have impeded the plan.

For months, Israel has said that its forces would remain in Lebanon until Hezbollah has been disarmed. Mr. Katz reiterated that in his statement on Friday, as the capture of the ridge underscored how entrenched the Israeli military has become in Lebanon, with little sign of an end to the occupation.

It remained unclear what Israel’s capture of the Ali al-Taher ridge would mean for the broader U.S. conflict with Iran. Tehran has insisted that any agreement to end that conflict must stop fighting on all fronts, including Lebanon.

Iran warned the United States on Thursday that Israel’s capture of the ridge would cross a red line and that Tehran would retaliate forcefully if the offensive continued, according to an Iranian official and a member of Iran’s Islamic Revolutionary Guards Corps. The officials, who asked not to be named because they were discussing sensitive issues, said the message was sent via Oman.

The Revolutionary Guards official said that roughly 70 to 100 Hezbollah members, along with Iranian military advisers, had been trapped inside the complex beneath the ridge as Israeli forces encircled it.

The Israeli military said on Thursday that it had established “operational control” over the ridge after an operation that began in June, when thousands of Israeli troops surrounded the underground facility, one of Hezbollah’s largest in Lebanon, and trapped dozens of militants inside.

The Israeli military said its soldiers had cleared Hezbollah militants from two underground routes beneath the ridge, killing some while others fled. Mr. Katz said on Friday that the military would now work to neutralize the tunnels and deploy around the ridge to maintain its hold and prevent Hezbollah from re-establishing itself there.

Sarit Zehavi, the president of the Alma Research and Education Center, an Israeli group focused on security along the northern border, said the capture of the ridgeline was significant but would not fundamentally alter the state of the conflict.

“I don’t feel that it’s a different day,” she said. “There is still a lot of work to do.”