“We are determined to get a cease-fire that brings the hostages home and to get it now, and the only reason that that wouldn’t be achieved is because of Hamas,” Mr. Blinken said at the start of a meeting in Tel Aviv with Isaac Herzog, the president of Israel. “There is a proposal on the table, and as we’ve said, no delays, no excuses. The time is now, and the time is now long past due to bring the hostages home to their families.”

Mr. Blinken made the same comments to reporters the previous evening outside a humanitarian aid warehouse in Zarqa, Jordan. Earlier this week, Mr. Biden spoke to the leaders of Qatar and Egypt to urge them to push Hamas to accept the terms, after Israel agreed to lower the required number of hostages released in the initial round to 33 from 40.

Prime Minister Benjamin Netanyahu of Israel supports the latest proposed deal, but at the same time he vowed on Tuesday to carry out a major offensive in the city of Rafah “with or without a deal” — a declaration that could make Hamas more wary of agreeing to the terms. Biden administration officials oppose a major ground assault in Rafah, where more than one million Palestinians have sought refuge during the war, and would prefer the Israeli military kill or capture Hamas leaders in more precise operations there.

Israeli officials say their objective is to eliminate four battalions of Hamas fighters in Rafah.

In November, Hamas freed more than 100 hostages during a seven-day cease-fire, but talks to try to get more hostages out of Gaza have been stalled for months. Israeli officials say Hamas took about 240 hostages in the Oct. 7 attacks last year, but some have died in captivity, and at least three were fatally shot by Israeli forces in Gaza.

Mr. Blinken discussed the hostage and cease-fire deal on the table in his nearly three-hour meeting with Mr. Netanyahu in Jerusalem on Wednesday, according to a summary from the State Department. He also spoke about efforts to increase humanitarian aid in Gaza and the U.S. government’s “clear position” on Rafah, the summary said.

Yair Lapid, the leader of the opposition in the Israeli Parliament, also spoke with Mr. Blinken. Afterward, Mr. Lapid said in a social media post that Mr. Netanyahu had “no political excuse” not to make a deal to declare a cease-fire and free the hostages, adding that “every hour is critical.”

After leaving Jerusalem, Mr. Blinken visited Kibbutz Nir Oz in the south, where he entered the burned-out home of the family of Kedem Siman Tov. The five members of the household, two parents and three young children, all American citizens, were killed in the Oct. 7 attacks. The father’s mother, Carol Siman Tov, also an American citizen, was killed in the same kibbutz.

Mr. Blinken then stopped at the inspection checkpoint at Kerem Shalom, a border crossing between Israel and Gaza. Flatbed trucks with bags of food aid bound for Gaza — onions, rice and cooking oil — were awaiting inspection.

Israeli officials said a new crossing into northern Gaza, near the Erez kibbutz, had just opened to allow aid deliveries, and that 30 trucks with goods from Jordan had rolled through the Erez border site earlier on Wednesday. The opening was promised weeks ago, but the Israeli military said it had to build inspection facilities and pave roads on both sides of the border before the crossing could be used by aid trucks.

Mr. Blinken has made humanitarian aid for residents of Gaza a theme of his stops in Israel and in Jordan the previous day. He visited an aid warehouse in Jordan on Tuesday evening where trucks were being loaded with food and medical aid to go to Erez for the initial opening on Wednesday.

”This is real and important progress,” he said, “but more still needs to be done.”

Earlier this week, Mahmoud Abbas, the president of the Palestinian Authority, turned down an offer to meet with Mr. Blinken in Riyadh, Saudi Arabia, according to two Palestinian officials and a State Department official who spoke on condition of anonymity because they weren’t authorized to communicate with the media.

Palestinian leaders are increasingly frustrated with Washington, especially after the United States blocked the United Nations from recognizing Palestine as a full member state.