By JULIA FRANKEL and MATTHEW LEE Associated Press

JERUSALEM (AP) — U.S. Secretary of State Antony Blinken was visiting fellow mediators Egypt and Qatar as he pressed ahead Tuesday with the latest diplomatic mission to secure a cease-fire in Gaza, even as Hamas and Israel signaled that challenges remain.

Hamas in a new statement called the latest proposal presented to it a “reversal” of what it agreed to previously, and accused the U.S. of acquiescing to what it called “new conditions” from Israel. There was no immediate U.S. response. Hamas has been designated as a terrorist organization by the United States, Canada and the European Union.

Israeli Prime Minister Benjamin Netanyahu, meanwhile, told families of fallen soldiers and hostages in Gaza that a key goal is to “preserve our strategic security assets in the face of great pressures from home and abroad.” The right-wing groups of families, who oppose a cease-fire deal, said Netanyahu told them Israel will not abandon two strategic corridors in Gaza whose control by Israel has been an obstacle in talks. Netanyahu’s office did not comment on their account.

The meeting came as Israel’s military said it recovered the bodies of six hostages taken in Hamas’ Oct. 7 attack that started the war, bringing fresh grief for many Israelis who have long pressed Netanyahu to agree to a cease-fire that would bring remaining hostages home.

Blinken’s meetings in Egypt and upcoming ones in Qatar come a day after he met Netanyahu and said the prime minister had accepted a U.S. proposal to bridge gaps separating Israel and Hamas. Blinken called on Hamas to do the same. But there still appear to be wide gaps between the two sides.

Pressure to seal a cease-fire deal has been especially urgent after the recent targeted killings of leaders of Hamas and Hezbollah in Iran and Lebanon, both blamed on Israel, and vows of retaliation that have sparked fears of a wider regional war.

Israel’s military said its forces recovered the six bodies in an overnight operation in southern Gaza, without saying when or how they died. Hamas says some captives have been killed and wounded in Israeli airstrikes, though returning hostages have talked about difficult conditions including lack of food or medications.

The recovery of the remains is also a blow to Hamas, which hopes to exchange hostages for Palestinian prisoners, an Israeli withdrawal and a lasting cease-fire.

The military said it had identified the remains of Chaim Perry, 80; Yoram Metzger, 80; Avraham Munder, 79; Alexander Dancyg, 76; Nadav Popplewell, 51; and Yagev Buchshtav, 35. Metzger, Munder, Popplewell and Buchshtav had family members who were abducted but freed during a November cease-fire.

Munder’s death was confirmed by Kibbutz Nir Oz, the farming community where he was among around 80 residents seized. It said he died after “months of physical and mental torture.” Israeli authorities previously determined the other five were dead.

Netanyahu said “our hearts ache for the terrible loss.” There were no immediate reports of any casualties among Israelis or Palestinians in the recovery operation.

Hamas is still believed to be holding around 110 hostages captured on Oct. 7. Israeli authorities estimate around a third are dead.

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Hamas-led terrorists burst through Israel’s defenses on Oct. 7 and rampaged across the south, killing some 1,200 people, mostly civilians, and taking around 250 people hostage. Over 100 hostages were released in exchange for Palestinians imprisoned in Israel during last year’s cease-fire.

Israel’s retaliatory offensive has killed over 40,000 Palestinians, according to Gaza’s Health Ministry, which does not distinguish between civilians and combatants in its count. The air and ground offensive has caused widespread destruction and forced the vast majority of Gaza’s 2.3 million residents to flee their homes, often multiple times. Aid groups fear the outbreak of diseases like polio.

An Israeli airstrike on Tuesday killed at least 12 people at a school-turned-shelter in Gaza City. The Palestinian Civil Defense, first responders operating under the Hamas-run government, said around 700 people had been sheltering at the Mustafa Hafez school. Israel’s military said the strike targeted Hamas fighters who had set up a command center inside the school.

“We don’t know where to go … or where to shelter our children,” said Um Khalil Abu Agwa, a displaced woman at the site.

An Israeli airstrike in Deir al-Balah hit people walking down the street and seven were killed, including a woman and two children, according to an Associated Press journalist who counted the bodies. More than 20 others were wounded.

Another airstrike in central Gaza killed five children and their mother, according to nearby Al-Aqsa Martyrs Hospital, where an AP journalist counted the bodies.

Lee reported from el-Alamein, Egypt. Associated Press reporters Wafaa Shurafa in Deir al-Balah, Gaza Strip; Samy Magdy in Cairo and Melanie Lidman in Jerusalem contributed to this report.