"We believe that the imam will keep his word," Jones told "Good Morning America" today. "We believe that proposal is still good."
But that proposal -- canceling the bonfire of Korans in exchange for moving the proposed Islamic center away from the site of the Sept. 11 terrorist attacks -- exists only in Jones' mind, said Musri, who is president of the Islamic Society of Central Florida.
"That offer wasn't on the table," Musri told "Good Morning America" today. "He stretched and exaggerated my statements."
"I told him, 'I did not even speak with the imam in New York, so how can I guarantee you?'" Musri said.
Musri said he was in the room with Jones when Gates called to impress upon Jones how dangerous the Koran-burning could be to U.S. troops serving in Muslim countries. He believed it was Gates' call that changed Jones' mind.
Jones said his conversation with Gates was "very short" but that the defense secretary was "very gracious" when he asked the pastor to cancel the burning.
Jones said he took Gates' concerns that U.S. service members would be put at risk "very, very seriously" and that "we absolutely would not want that to happen."
"I tried to close the deal," Musri said, recalling how he told Jones that if he did not cancel there could be riots today, as Muslims celebrate the end of Ramadan.
"I told him I'm willing to make contact as an imam with the imam in New York, Muslim to Muslim," Musri said. "And ask to schedule a meeting."
But Jones, who repeatedly mispronounced the Muslim honorific as "iman," said today that he confirmed the exchange several times with Musri Thursday and that the two men were clear on the proposal that he thought would "make everyone happy."
"There is absolutely no possibility that I misunderstood him," Jones said. "If he is saying that, then he is lying."
"I had witnesses in my office," he said. "We repeated it several times."
Gen. David Petraeus, the top U.S. commander in Afghanistan, weighed in on the controversy, telling ABC News that "there has been some damage done" by the mere threat of Jones' leading his worshippers in burning Korans.
"There are already in a sense images, if you will, implanted in minds," he said, "albeit not with photos of something as inflammatory as the burning of a Koran."
Even Donald Trump joined the conversation Thursday when he offered to buy out one of the investors of the New York site for 25 percent more than they had paid.
Rauf told ABC News' Christiane Amanpour that the move of the center in New York would have serious consequences in the Muslim world.
"Let's say we moved under this current circumstance with this dialogue," said Rauf. "What will be the headline tomorrow in the Muslim world?"
"'Islam under attack in America.' That's the theme of it. 'Mosque forcibly removed by whatever.' That will feed the radicals. So diffusing terrorism is a necessity for our national security," he said.
The developer of the project Rauf calls a "multifaith community center" also issued a denial that it would be moved.
"The Muslim Community Center called Park51 in Lower Manhattan is not being moved," read a statement from SoHo Properties. "The project will proceed as planned."
Jones told "Nightline" Thursday that despite cancelling the burn, events have upheld his dim view of Islam.