The U.S. government is making an intense effort to persuade Israel and Hamas to resume negotiations so they can once again pause hostilities and exchange more prisoners for hostages, a White House spokesman said on Sunday.

“We are still working it really hard, hour by hour, to see if we can get the sides back to the table and see if we can get something moving,” John F. Kirby, the strategic communications coordinator at the White House National Security Council, said on NBC’s “Meet the Press.” “We would like that to happen today. But honestly, I just don’t know.”

In appearances on several Sunday talk shows, Mr. Kirby emphasized that Hamas was to blame for the breakdown in talks, saying that it had not lived up to the terms of its original agreement to begin handing over captives held in Gaza.

He said Hamas had failed to produce a list of women and children who could be released in addition to the 105 hostages who were freed during the original pause in fighting. Among those still held are eight or nine Americans. Osama Hamdan, a representative for Hamas in Lebanon, said on Sunday that negotiations over the hostages would not resume until the Israeli assault stopped.

Israel has since resumed its attacks on Hamas, and Mr. Kirby urged it to avoid civilian casualties, while crediting its forces with making efforts to do so. He said Israeli authorities had been open to U.S. advice about how to make their assault more precise.

“We believe that they have been receptive to our messages here in terms of trying to minimize civilian casualties,” he said on ABC’s “This Week.” He noted that Israel had published a map directing civilians to what it said were safe zones.

“There’s not a whole lot of modern militaries that would do that, I mean, that is, to telegraph their punches in that way,” he said. “So they are making an effort.”

President Biden and his administration have sought to straddle a careful line nearly two months after the Oct. 7 terrorist attack in which Hamas killed an estimated 1,200 people in Israel and took about 240 more hostage. While supporting Israel’s right to defend itself, the administration has also sought to restrain Israel from what it believes would be going too far in its response.

That led to criticism from both the left and the right on Sunday, as some Republicans complained that Mr. Biden’s team was trying to hold Israel back, while some liberal Democrats complained that it was not doing that enough.

Senator Lindsey Graham, Republican of South Carolina, singled out Defense Secretary Lloyd J. Austin III. In a speech on Saturday, Mr. Austin warned that Israel should protect civilians in Gaza and prevent violence against Palestinians by Jewish settlers in the West Bank, because otherwise “you replace a tactical victory with a strategic defeat.”

Speaking on CNN’s “State of the Union,” Mr. Graham castigated Mr. Austin, a retired four-star general who fought in Iraq. “He’s so naïve; I mean I just lost all confidence in this guy,” Mr. Graham said.

“If we were attacked like this, which we were on 9/11, if somebody called for us within two months to have a cease-fire against Al Qaeda, we’d have laughed them out of town, we’d have run them out of town,” Mr. Graham added. “Secretary Austin is telling Israel things that are impossible to achieve.”

Mr. Graham said his solution to the hostage impasse would be to threaten Iran, the sponsor of Hamas. “I would go to Iran and say listen, you need to tell Hamas to let these hostages go,” he said. “If you don’t, you’re going to start paying a heavier price.”

On the other side of the ideological spectrum, Representative Pramila Jayapal, Democrat of Washington, said on the same program that the Biden administration had a responsibility to stop Israel from killing so many civilians.

“The United States cannot be backers of this kind of indiscriminate bombing — that is my firm belief,” she said. “We should have conditions on military aid in the same way that we do for every other country.”

While the White House blamed Hamas for the breakdown in hostage talks, Ms. Jayapal faulted Israel.

“Qatar has said that Hamas is still at the table,” she said, referring to the Persian Gulf emirate that has served as the intermediary for the talks. “Israel should still be at the table. In fact, some of the Israeli hostages are saying that Israel should still be at the table, because this is complex negotiation and it doesn’t happen unless both sides are willing to come to some kind of an agreement.”

Hwaida Saad contributed reporting.

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