John F. Kirby, a White House spokesman, said the president wants to see “concrete tangible steps” to reduce the violence against civilians and increase access for humanitarian aid to Gaza. He said the White House expects Israel to make announcements of specific changes within hours or days.

But Mr. Kirby would not outline specific metrics for judging Israel’s response or what Mr. Biden would do if not satisfied. “What we want to see are some real changes on the Israeli side and, you know, if we don’t see changes from their side there will have to be changes from our side,” he said.

The president has long resisted curbing the arms flow to Israel to influence its conduct of the war, with aides arguing that many of the munitions sent are air defense missiles. But even some of Mr. Biden’s close Democratic allies have increasingly come around to the view that Washington should exercise more control over the weaponry, including Senator Chris Coons, a fellow Democrat from Delaware and confidant of the president.

“I think we’re at that point,” Mr. Coons said on CNN on Thursday morning, adding that if Mr. Netanyahu were to order the Israeli military into the southern Gaza city of Rafah in force and “drop thousand-pound bombs and send in a battalion to go after Hamas and make no provision for civilians or for humanitarian aid, that I would vote to condition aid to Israel.”

Mr. Netanyahu did not immediately release a description of the call, but in other comments on Thursday appeared unbowed. In a meeting in Jerusalem with visiting Republican lawmakers organized by the American Israel Public Affairs Committee, known as AIPAC, the prime minister pushed back strongly against Mr. Biden’s insistence on a two-state solution to the Palestinian conflict.

“There is a contrary move, an attempt to force, ram down our throats a Palestinian state, which will be another terror haven, another launching ground for an attempt, as was the Hamas state in Gaza,” Mr. Netanyahu said. “That is opposed by Israelis, overwhelmingly.”

In a separate video statement, he focused on the threat he sees from Iran. “For years Iran has been acting against us, both directly and though its proxies, and therefore Israel is acting against Iran and its proxies, in both defensive and offensive operations,” he said, referring to an Israeli airstrike that killed seven Iranian military officers in Syria this week.

“We will know how to defend ourselves,” he added, “and we will operate according to the simple principle by which those who attack us or plan to attack us — we will attack them.”

The White House said that Mr. Biden stood by Israel against Iran during his Thursday call with Mr. Netanyahu, which Vice President Kamala Harris, Secretary of State Antony J. Blinken and Jake Sullivan, the national security adviser, joined in.

“The two leaders also discussed public Iranian threats against Israel and the Israeli people,” the White House statement said. “President Biden made clear that the United States strongly supports Israel in the face of those threats.”

The president’s threat to condition American support on Israeli conduct came under rising pressure from his own party. Some of former President Barack Obama’s old team have grown more outspoken in castigating Mr. Biden for not doing more to restrain Mr. Netanyahu, who goes by the nickname Bibi, and the Israel Defense Forces, or I.D.F., saying that the president’s expressed outrage was meaningless otherwise.