Protesters in Tel Aviv and around the world Saturday called on Israeli leaders to accept the latest road map for a cease-fire and the return of hostages in Gaza, a day after President Biden said it was time for the war to end.

The Hostages and Missing Families Forum in Israel said it was launching “an emergency operation” to pressure members of the government to accept the declaration outlined by President Biden on Friday. The plan would begin with an immediate, temporary cease-fire and work toward the return of all hostages, a permanent end to the war and the reconstruction of Gaza.

“The Forum demands the return of all the hostages, some for rehabilitation and others for burial, and not to miss the opportunity that has arisen to bring them home,” the group said in a statement on social media.

The group demanded an “immediate approval of the deal,” the statement said, adding, “Don’t lose this moment!”

Mr. Netanyahu was still calling for the complete destruction of Hamas and the freeing of all hostages before ending the war. And two of Mr. Netanyahu’s far-right coalition partners — Bezalel Smotrich and Itamar Ben-Gvir — threatened to quit his government should he move forward with the proposal.

The debate over the latest proposal gave new life to protests held every Saturday night in Tel Aviv. Thousands of demonstrators rallied in the streets there and in other parts of Israel on Saturday evening in support of the proposal.

Some protesters covered themselves in fake blood, and others walked through the streets holding the Israeli flag and signs that read “Bring Them Home,” referring to the hostages. Haaretz, an Israeli newspaper, reported that protesters blocked traffic in northern Israel, and at least three people have been detained.

Haaretz also reported that thousands of demonstrators rallied near Mr. Netanyahu’s house in Caesarea, a coastal town located midway between Tel Aviv and Haifa.

Protesters also gathered in Rome, Paris and Jakarta on Saturday.

The United States also continued its efforts to push the region to work toward a cease-fire in Gaza.

Secretary of State Antony J. Blinken spoke on Saturday with the Egyptian foreign minister, Qatar’s prime minister and Qatar’s minister of foreign affairs. Egypt and Qatar have been working to help broker an agreement. In his phone calls, Mr. Blinken spoke about the urgent need for a cease-fire and called on Hamas to accept the deal without delay, said Matthew Miller, a spokesman for the State Department.

Aaron Boxerman contributed reporting.