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US Secretary of State Antony Blinken on Friday said Hamas and Israel were in the final stages of drawing up a ceasefire deal.
Using an American football analogy, Mr Blinken said the goal was in sight.
“I believe we’re inside the 10-yard line and driving towards the goal line on getting an agreement that would produce the ceasefire, get the hostages home and put us on a better track to try to build lasting peace and stability,” Mr Blinken told the Aspen Security Forum.
“We also know that with anything, the last 10 yards are often the hardest.”
He said some issues remained unresolved, which still "need to be negotiated".
White House National Security Council adviser Jake Sullivan later seconded those remarks, adding that "there are some technical details to be worked out about the phase one to phase two sequence" of the ceasefire deal.
"I have learnt the hard way never to use the word 'optimism' in the same sentence as the Middle East. And so what I will say is that I think we have our best opportunity now that we have had since the last brief hostage deal in November," Mr Sullivan said.
Israeli Prime Minister Benjamin Netanyahu is due to visit Washington next week, where Mr Sullivan says discussions with President Joe Biden will focus strictly on those negotiations.
The US officials were speaking in Colorado for the final day of the forum. A group of about 15 protesters gathered at the entrance to the resort where the conference is taking place, accusing the Biden administration of enabling genocide.
Asked about what global crises aren't getting enough attention, Mr Blinken pointed to the civil war in Sudan.
"Sudan right now is probably the worst humanitarian crisis in the world, and yet it's not getting the attention it deserves," Mr Blinken said.
On Iran, Mr Blinken reiterated previous US government assessments that Tehran could now produce fissile material for nuclear weapons within one or two weeks, if it chose to.
