Jones appeared with Imam Muhammad Musri from the Islamic Society of Central Florida, who has been meeting with Jones over the past two days to convince him not to burn Korans.
Musri, however, said he got a commitment only that Rauf would meet with the two "to discuss and come to a decision on relocating the mosque in New York." Musri was the one who spoke with Rauf's office.
Musri and Jones said they are flying to New York on Saturday, Sept. 11, to met with Rauf.
Several news outlets are reporting that Rauf has denied that he agreed to move the Islamic center.
Musri told CNN after the press conference that he spoke with Daisy Khan, Rauf's wife. He also said they have not yet bought their plane tickets to New York or set up a definite time for their meeting.
The Pentagon confirms that Defense Secretary Robert Gates called Jones to urge him not to burn Korans.
Late update: There's still a lot of confusion. Rauf now says he was "surprised" by the announcement by Jones, but hasn't mentioned whether they're meeting. For the latest, check our live-updating wire.
Late late update: Watch Jones' announcement: