The pair have been named by the Israeli prime minister's office as Judith Raanan and her daughter Natalie Raanan.

Judith is believed to be aged around 60 while Natalie is 17 years old.

The PM's office said: "This evening, Judith Tai Raanan and Natalie Shoshana Raanan were released from the hands of the terrorist organisation Hamas."

Its statement said they were kidnapped by Hamas on Saturday 7 October while they were staying at Nahal Oz kibbutz.

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Both of them hold Israeli citizenship and were on a trip to Israel from their home in Chicago to celebrate the Jewish holidays.

They were seized during a major raid by Palestinian militants from Gaza who stormed the border into southern Israel and killed hundreds of Israelis.

Hamas fighters captured 203 hostages and brought them back to Gaza as part of their deadly attack.

The Israeli PM's office said Brigadier General Gal Hirsch, together with Israeli troops, "received" the mother and daughter "at the border of the Gaza Strip".

It said the women were on their way to a meeting point at a military base in the centre of the country, where their family members were waiting for them.

Hamas said the pair were freed for "humanitarian reasons".

Abu Ubaida, of Hamas's armed wing, said the release was in response to Qatari mediation efforts and to "prove to the American people and the world that the claims made by [Joe] Biden and his fascist administration are false and baseless".

'Anguish turned to joy'

A former Middle East correspondent for NBC, Martin Fletcher, whose wife is related to the freed hostages, described the events as "a miracle".

Speaking to NBC News, Mr Fletcher said: "We were talking about it yesterday... would they be human shields? Would they be killed in the invasion? Nothing good could possibly happen.

"Before, [my wife] was crying tears of anguish - now I guess she is crying tears of joy - and my wife is not a sentimental woman.

"And, you know, she was the first to say: 'That's just our family - what about the rest?'."

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Biden 'overjoyed'

In a White House statement following their release, US President Joe Biden said: "Our fellow citizens have endured a terrible ordeal these past 14 days, and I am overjoyed that they will soon be reunited with their family, who has been wracked with fear."

Mr Biden added the US had "been working around the clock" to free American captives and "have not ceased efforts to secure the release of those who are still being held".

He thanked Qatar and Israel for their partnership in securing the pair's freedom.

The International Committee of the Red Cross said it "helped facilitate" their release by "transporting the hostages" across the border.

Qatar said it would continue talks with Israel and Hamas in the hope of liberating all the hostages "with the ultimate aim of de-escalating the current crisis and restoring peace".

Speaking at a news conference, US Secretary of State Antony Blinken said there are "still 10 additional Americans who remain unaccounted for" as he called for the release of every hostage being held in Gaza.

Hostage release a 'first step'

The release of the mother and daughter was "a first step and discussions are ongoing for more releases", a source briefed on the negotiations to free hostages told the Reuters news agency.

Earlier on Friday, Israel said 20 of the hostages being held by Hamas were under 18, while between 10 and 20 were over 60.

On Monday, senior Hamas official Khaled Meshaal had demanded 6,000 Palestinian men and women detained in Israel's jails be released in exchange for the captives in Gaza.

In response to the hostage situation and the surprise assault, Israel retaliated by bombarding the Gaza Strip.

The Gaza health ministry said at least 4,137 people have been killed in Gaza since the latest war began, the majority of them women, children and older adults. More than 13,000 others have been injured.

Israel has said its aim for the Gaza onslaught is eradicating Hamas and Israel Prime Minister Benjamin Netanyahu said Israel would "do everything it [could] to keep civilians out of harm's way" when speaking to Mr Biden on Thursday.

In a statement issued late on Friday, the prime minister remained defiant saying: "Two of our abductees are at home. We are not giving up on the effort to return all abducted and missing people.

"At the same time, we'll continue to fight until victory," he added.

Israel said 1,400 of its citizens were killed in the weekend raid - including 260 at a music festival.