When Abood Okal, a 36-year-old American father trapped in Gaza, received word from U.S. State Department officials informing him the Rafah crossing into Egypt would likely open on Oct. 21 for the first time since Hamas launched a surprise terror attack on Israel two weeks before, he thought the nightmare he has been enduring with his wife and young son might finally be coming to an end.

He took his family to the gate and waited all day, his lawyer Sammy Nabulsi said. But while humanitarian aid was allowed to enter into Gaza, no one was allowed to exit.

In the days that followed, the State Department blamed a single culprit: Hamas. However, according to emails and messages reviewed by ABC News, U.S. officials privately provided a different explanation to Okal, saying their inability to cross the border was the result of a failure to lock up a diplomatic agreement among Israel, Egypt and the terrorist group to grant Americans safe passage out of Gaza.

"There's more than one sticking point. We need Egypt, Israel, and the DFA to all agree," a senior State Department official wrote in an email sent Saturday to Nabulsi, presumably using the acronym "DFA" to refer to the de facto authorities controlling Gaza: Hamas. "We are very close to agreement with two of the three. And we are working the third very hard."

The senior official added in the same email to Nabulsi that U.S. officials had advised consular officers working with Americans in Gaza "not to issue any additional statements advising Americans of opportunities to cross Rafah until we have a clear 'yes' from all actors."

As of midday Wednesday, Nabulsi and Okal say they haven't received any meaningful update from the State Department.

"We are staying in place, trying not to leave as the airstrikes have been intensifying. Last night we could still hear bombardment all around us," Okal said in an audio recording shared with ABC News on Thursday. "Every day we are concerned it's going to become too late."

The State Department declined to comment on any private correspondence, but spokesperson Matthew Miller has publicly acknowledged that the department advised Americans in Gaza that the Rafah gate would possibly be opened for them on a few previous occasions when it turned out not to be the case, and said the department had sent a message on Wednesday to them saying officials were "continuing to work out a solution."

"We have been making progress," Miller said during a press briefing on Thursday. "It's something that we are focused on and hope to have American citizens and other foreign nationals able to move through in the coming days."

While the State Department's explanation of the dynamics at the Rafah crossing have become more nuanced, in the hours after Nabulsi was told there were multiple factors preventing Okal and his family from leaving Gaza, Secretary of State Antony Blinken blasted only Hamas for standing in the way.

"So really, the ball is in Hamas' court, in terms of letting people who want to leave, civilians from third countries including Americans get out of Gaza," Blinken said in a televised interview.

On Monday, Miller echoed Blinken, saying Hamas was the only entity standing in the way.

"The reports we were given on the ground is that Hamas was there blocking anyone from coming through the gate from the Gaza side out to the Egyptian side," he said.

"We do believe that Egypt is ready to process American citizens if they can make it to Egyptian authorities. Hamas just has to stop blocking their exit," Miller added.

But video and images sent by Okal on Saturday appear to show no one blocking the Rafah passage. Only a gathering of people, including women and children, standing up against a closed gate with pieces of luggage, was visible in those images and video.

"Usually we go through this gate," a voice narrating a video clip says. "No one can walk here. If you try to walk here. Basically if you try to walk there, basically you'll stop at the actual border and the Egyptians will shoo you back."

State Department officials have walked back some of their initial allegations on Hamas' barricading of foreign nationals.

"Hamas has had no one there manning the border station. Remember that this is an area that is administered by Hamas," Miller said in an interview on Wednesday. "So there has been a problem in getting people through the Gaza side into the no man's land where they can ultimately get across to the Egyptian side to be processed."

Miller did not explain why Hamas' absence from the border station prevented Americans from leaving Gaza but has so far not hindered the flow of limited humanitarian aid into the area.

"I don't know actually if someone is opening the other side of the vehicle gate that these trucks are going through. I assume it's Hamas, but I don't know that for a fact," Miller said on Thursday of the separate portal at the Rafah crossing used to move convoys into Gaza.

"We are pursuing every possible alternative available to get those American citizens out," he said.

Speaking on the condition of anonymity, a State Department spokesperson signaled that negotiations with all parties involved in opening the Rafah crossing to foreign nationals were still ongoing.

"We're dealing with Israel, Egypt, and Hamas, and we're not talking directly to Hamas. Egypt can send messages to Hamas, Qatar can send messages to Hamas. But you can imagine how difficult every little thing is, every bit of this is complicated," the spokesperson said. "It's like unlocking a puzzle where you unlock a layer that can unlock one little piece of it. And then another obstacle pops up and you've got to go figure out with all the parties, how to unlock that piece. We're making progress and I think we'll get there, but it's difficult."

While those talks drag on, Okal and his family -- as well as the estimated 500-600 American citizens in Gaza with no way out -- continue to suffer.

"We've been trying to stay strong, but it hasn't been easy. Airstrikes have intensified in the past few days," Okal said in a voice memo that he said was recorded in the Gaza city of Rafah on Wednesday.

Okal said that he and his wife are trying to shelter their one-year-old son from the impacts of the war -- but they can only do so much.

"Unfortunately, yesterday we ran out of milk for him," Okal said. "We opened the last box and basically tonight we will be completely out. It will be his first night ever in his entire life to go to sleep without having milk. So we're hopeful that that will not be too bad of a night."