Hamas said on Tuesday that after an Israeli airstrike it had "lost contact" with the captors of an Israeli-American hostage in Gaza, whose release takes centre stage in Israel's latest proposal for a renewed ceasefire.

Israeli Prime Minister Benjamin Netanyahu visited northern Gaza on Tuesday, his office announced, as the military kept up the offensive it resumed on March 18, effectively ending a two-month ceasefire.

"We announce that we have lost contact with the group holding soldier Edan Alexander following a direct strike on their location. We are still trying to reach them at this moment," Abu Obeida, spokesman for Hamas's military wing the Ezzedine Al-Qassam Brigades, said on his Telegram channel.

The military wing later released a video addressed to the families of the remaining hostages, warning them that their loved ones were likely to return in coffins if Israel keeps up its bombardment of the territory.

Over video images of masked militants carrying black coffins out of white vans in the darkness, the video carried a subtitled message in English, Arabic and Hebrew.

"Be prepared. Soon, your children will return in black coffins with their bodies torn apart by shrapnel from your army's missiles," the message warns.

Hamas's armed wing released a video on Saturday showing Alexander alive, in which he criticised the Israeli government for failing to secure his release.

Alexander appeared to be speaking under duress in the footage, making frequent hand gestures as he criticised Netanyahu's government.

It is unclear when the video was filmed.

Alexander was serving in an elite infantry unit on the Gaza border when he was abducted by Palestinian militants during their October 2023 attack.

The soldier, who turned 21 in captivity, was born in Tel Aviv and grew up in the US state of New Jersey, returning to Israel after high school to join the army.

Hamas said on Monday it had received a new truce offer from Israel that foresees the release of 10 living hostages, starting with Alexander, in exchange for a 45-day ceasefire.

A Hamas official said the Israeli proposal called for Alexander's release on the first day of the ceasefire as a "gesture of goodwill."

It was delivered to the group's delegation in Cairo by Egyptian officials over the weekend and a senior Hamas official said the group would "most likely" respond within 48 hours.

Out of 251 hostages taken during Hamas's October 2023 attack, a total of 58 remain in captivity, including 34 the Israeli military says are dead. (AFP)