The Biden administration in Washington has welcomed the deal between Israel and Hamas which it said should result in the release of additional Americans who had been held hostage.
However US president Joe Biden said he “will not stop until they are all released”.
He said that as president, he had no higher priority than ensuring the safety of Americans held hostage around the world.
“That’s why – from the earliest moments of Hamas’s brutal assault – my national security team and I have worked closely with regional partners to do everything possible to secure the release of our fellow citizens. We saw the first results of that effort in late October, when two Americans were reunited with their loved ones.”
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He said the deal reached on Tuesday “should bring home additional American hostages”.
The New York Times, citing unnamed White House officials, said the agreement would include the release of three Americans: two women and a toddler.
The officials said they would continue to push for the release of all US hostages.
It said the deal approved by the Israeli Cabinet on Tuesday came after a “secret cell” of aides to Mr Biden worked hard over weeks in talks involving Qatar, Egypt and Israel.
The US secretary of state Antony Blinken said the agreement was “the result of tireless diplomacy and relentless effort across the (state) department and broader United States government”.
[ Fifteen reported killed in Israeli strike on apartment in GazaOpens in new window ]
He said he appreciated “the leadership and ongoing partnership of Egypt and Qatar in this work”.
“While this deal marks significant progress, we will not rest as long as Hamas continues to hold hostages in Gaza. My highest priority is the safety and security of Americans overseas, and we will continue our efforts to secure the release of every hostage and their swift reunification with their families.”
The Biden administration had fully backed Israel following the attack by Hamas on the country in October.
However, it had urged it to operate within the laws of warfare.
The New York Times again citing White House officials said that over the last several weeks, Mr Biden had concluded that convincing Israeli prime minister Binyamin Netanyahu to accept longer a pause in the fighting in Gaza would require linking any ceasefire to a deal to free hostages being held by Hamas in Gaza.
It said that the president had made that case with increasing urgency to Mr Netanyahu during 13 calls since the Hamas attacks and a face-to-face meeting in Israel.
As the number of Palestinian casualties increased in Gaza, Mr Biden has also been coming under pressure from progressives and young people over his full support for Israel.
Disenchantment with the president among key groups in his overall Coalition of supporters could prove costly for Mr Biden who is now less than a year away from running again for the White House.
Mr Biden, meanwhile, seems intent on trying to inject more urgency into moving on from any new ceasefire in Gaza to seeking greater peace for the entire Middle East.
The president wrote in an opinion column in the Washington Post last Sunday wrote: “Our goal should not be simply to stop the war for today.”
“It should be to end the war forever, break the cycle of unceasing violence, and build something stronger in Gaza and across the Middle East so that history does not keep repeating itself.”
On Tuesday night Mr Biden said it was “important that all aspects of this deal (between Israel and Hamas) be fully implemented”.
