Qatari mediators have held urgent calls with Hamas officials to try to negotiate freedom for Israeli women and children seized by the terrorist group and held in Gaza in exchange for the release of 36 Palestinian women and children from Israel's prisons, a source briefed on the talks told Reuters.

The ongoing negotiations, which Qatar has been conducting in coordination with the United States since Saturday night, are "moving positively" said the source, who has been briefed on them.

But there are no signs of breakthroughs as both sides dig in.

Qatar has been in touch with Hamas officials in Doha and Gaza, the source said, after the terrorist group assaulted Israel from Gaza on Saturday, storming into towns, killing more than 700 Israelis, and escaping with dozens of hostages.

The exact number of Israeli women and children hostages Hamas is offering in the potential exchange of 36 Palestinian women and children prisoners Hamas identified is not clear, the source said.

Details about negotiations focusing on the release of 36 Palestinians from Israeli jails have not previously been reported.

The number of Israeli hostages held in Gaza also remains unclear, but it is widely believed that Hamas seized women, children, elderly people and soldiers on Saturday.

A Palestinian official, familiar with mediation efforts with Hamas and Israel in the past, told Reuters that Qatar and Egypt have been in contact with the group but the intensity of the fighting cast shadows over any potential breakthrough.