President Biden and his top aides have engaged in an increasingly awkward dance in recent days, prodding Israel to change its tactics in the war in the Gaza Strip while still offering it robust public support.

Mr. Biden said last week that Israel was losing international support because of its “indiscriminate bombing” of Gaza, a much more critical assessment than his earlier public statements urging greater care to protect civilians. On Monday, Defense Secretary Lloyd J. Austin III, in his second visit to Israel since the Hamas-led Oct. 7 attacks, sought to take the temperature down a few degrees.

Meeting with Prime Minister Benjamin Netanyahu, Defense Minister Yoav Gallant and other top Israeli officials, Mr. Austin discussed in detail how Israeli forces will transition to the next phase of the war, a shift U.S. officials believe will lower the risk to civilians.

Mr. Austin is a retired four-star head of the Pentagon’s Central Command, overseeing U.S. military operations in the Middle East, and his word carries weight with Israel’s leaders, many of whom, like Mr. Gallant, are also former army generals.

Speaking to reporters after daylong meetings, Mr. Austin called U.S. support for Israel “unshakable,” and endorsed its campaign to destroy the ability of Hamas, which controls Gaza, to wage military operations in the difficult urban terrain. But he also repeated a message he has increasingly made of late: Israel will be left less secure if its combat operations turn more Palestinians into Hamas supporters.

“Israel has every right to defend itself,” he said, standing alongside Mr. Gallant. “As I’ve said, protecting the Palestinian civilians in Gaza is both a moral duty and a strategic imperative.”