Prime Minister Benjamin Netanyahu said on Thursday that the Israeli military would keep striking Hezbollah militants in Lebanon with “all our might,” even as the United States, its European allies and several Arab states worked furiously to negotiate a three-week cease-fire.

Mr. Netanyahu’s comments came as he arrived in New York ahead of a planned speech to the United Nations General Assembly, where world leaders have been issuing urgent calls for cease-fires in the Gaza Strip and Lebanon, warning of the risk of a wider Middle East war.

Despite those warnings, Israel said on Thursday that it had killed another high-ranking Hezbollah commander in a bombing in Beirut and had struck Hezbollah targets elsewhere in Lebanon after the militant group, which is backed by Iran, fired 45 rockets into northern Israel. None of them caused damage or injuries.

The Israeli military said it had also bombed a school compound being used as a shelter in Gaza, which it said housed a Hamas command-and-control center. It was the latest in a series of Israeli strikes on former schools. Palestinian Civil Defense officials said 15 people, including women and children, were killed and dozens of others were wounded.

While Mr. Netanyahu stopped short of rejecting a truce with Hezbollah, many Israeli lawmakers and members of his government were quick to dismiss the proposal.