Prime Minister Benjamin Netanyahu welcomed her home, saying the “achievement” by Israel’s security forces “illustrates our commitment to free all the hostages”.

He also rejected calls for a ceasefire to facilitate the release of captives or end the war, which he has said will be long and difficult.

“Calls for a ceasefire are calls for Israel to surrender to Hamas,” he told a press conference. “That will not happen.”

Israel says its war can both destroy Hamas and rescue hostages in Gaza

He also said he has no plans to resign in the face of mounting anger over the failure of Israel’s vaunted security forces to prevent the worst surprise attack on the country in a half-century that killed 1,400 people.

Hamas and other militant groups are believed to be holding some 240 captives, including men, women and children.

Hamas, which has released four hostages, has said it would let the others go in return for thousands of Palestinian prisoners held by Israel, including many implicated in deadly attacks on Israelis.

Israel has dismissed the offer, and Netanyahu said the ground invasion “creates the possibility” of getting the hostages out, adding that Hamas will “only do it under pressure”.

Hamas released a short video Monday purporting to show three other female captives. One of the women delivers a brief statement – likely under duress – criticising Israel’s response to the hostage crisis.

The three women in the video were seen sitting on plastic chairs against a tile wall at an undisclosed location.

One of them, speaking in Hebrew, urges Netanyahu to agree a prisoner exchange for the release of all captives.

She makes agitated hand gestures and starts shouting, almost screaming by the end of the statement.

The two women sitting either side of her remain silent but on edge.

‘Viet Cong times 10’: underground warfare awaits Israeli troops in Gaza

It was not clear when the Hamas video was made. In a statement, Netanyahu named the hostages as Yelena Trupanov, Daniel Aloni and Rimon Kirsht.

Netanyahu denounced the anguished images of the three women as “cruel psychological propaganda”.

Following the release of the video, friends and relatives of the three Israeli women came together to call on the international community to push harder for their release.

“This is our first proof of life,” Shahar Cohen, a friend of the Trupanov family, shouted in front of dozens of Israeli and foreign journalists in Tel Aviv late Monday.

“As both an Israeli and an American citizen, I’m personally asking you, President Biden, please, do any and everything in your power to bring everyone home now.”

Amos Aloni, whose daughter Daniel appeared in the video, told reporters that he and his wife were shocked when she appeared on TV but also felt “relief from her being alive and seeing her”.

Hamas’ armed wing has said that “almost 50” of the hostages had been killed in Israeli strikes, which according to the Hamas-run health ministry have also killed more than 8,300 people in Gaza, more than half of them women and children.

Earlier on Monday, the family of German-Israeli Shani Louk said they had been notified that she had died after being seized by gunmen at a music festival where at least 260 people were killed.

Hamas released a video showing Israeli-French hostage Mia Shem on October 16. Those images were condemned by the Israeli and French governments.

The Israeli military has been vague about its operations inside Gaza, including the location and number of troops. Israel has declared a new “phase” in the war but stopped short of declaring an all-out ground invasion, even as it has deployed tens of thousands of troops to the border.

The movements of recent days, including larger ground operations both north and east of Gaza City, point to a focus on the city.

Israel says much of Hamas’ forces and militant infrastructure, including hundreds of kilometres of tunnels, are in Gaza City, which before the war was home to over 650,000 people, a population comparable to that of Washington DC.

Additional reporting by Agence France-Presse