(CNN) -- A Florida pastor who called off a Quran burning said late Thursday he would "rethink our position" after a Muslim leader said the minister incorrectly announced that the proposed Islamic center near New York's ground zero would be moved as part of a deal.

The dramatic development was one of several twists on a day when President Barack Obama and Defense Secretary Robert Gates urged the Rev. Terry Jones to call off the Saturday event, timed for the ninth anniversary of the September 11, 2001, terrorist attacks.

During the afternoon, Jones canceled his plan to burn copies of the Quran, based on what he said were assurances from a local Muslim leader that the Islamic center in New York would be moved -- an assertion rejected by the center's visionary in New York.

Jones, leader of the Gainesville, Florida-based Dove World Outreach Center, announced he will travel Saturday to New York to meet with the religious leader behind the planned center, Imam Feisal Abdul Rauf, about a new location.

But that, too, was questioned.

Rauf and Imam Muhammad Musri, a Florida Muslim leader who appeared with Jones, said later no agreement on a meeting or relocation of the mosque had been reached.

Jones insisted the church "put a temporary hold" on the Quran burning event after he had been told by Musri of a deal to move the New York mosque.

"I am actually very disappointed and very shocked because if this turns out to be true, he [Musri] clearly, clearly lied to us," Jones said Thursday evening.

Wayne Sapp, associate pastor of the small church, said that the Quran burning scheduled for Saturday was postponed until the proposed meeting in New York is confirmed. The church will wait 24 hours to confirm the meeting will take place before making any further decision about the Quran burning, Sapp said.

Rauf issued a statement a few hours earlier.

"I am glad that Pastor Jones has decided not to burn any Qurans. However, I have not spoken to Pastor Jones or Imam Musri. I am surprised by their announcement. We are not going to toy with our religion or any other. Nor are we going to barter. We are here to extend our hands to build peace and harmony."

The back-and-forth over the mosque location and the meeting continued into the evening Thursday. Jones insisted he had been told of a deal on moving the center, but Musri said instead he was brokering a meeting with Rauf.

"We are canceling the event because they have agreed to move the ground zero mosque," Jones said, claiming his announcement was based on several conversations with Musri.

But the latter said he had not spoken with Rauf and was not authorized to say the Islamic center would be moved. Jones may have "stretched" their conversations to say there was a deal, Musri told CNN.

He said he believes Jones knows there was no deal on the mosque and may be using Thursday's controversy to gain leverage on the proposed mosque.

Rauf's office told him they would welcome Jones to a meeting if he canceled the Quran burning, Musri said, adding it was his understanding from Jones that he canceled the Quran burning because of a Muslim holy day.

Sharif El-Gamal, developer of Park51, denied there had been a change in plans for the New York center.

"It is untrue that the community center known as Park51 in lower Manhattan is being moved," El-Gamal said in a statement. "The project will proceed as planned. What is being reported in the media today is a falsehood."

Jones, pastor of the Gainesville-based Dove World Outreach Center, said he felt a relocation of the mosque "would be a sign from God."

Musri, with the Islamic Society of Central Florida, told CNN that he hoped the Saturday meeting will, in fact, take place.

Jones' plans to burned Qurans had set off a firestorm of concern, including from U.S. military leaders who said the event would imperil the lives of troops abroad.

The pastor told reporters Thursday that he took a phone call from Gates, who "was very gracious and encouraged us not to continue." The call was later confirmed by CNN.

Also Thursday, real estate mogul Donald Trump offered to buy the lower Manhattan site where the Muslim group plans to build an Islamic community center, for 25 percent more than the current owners paid for it.

Trump made the offer Thursday in a letter to Hisham Elzanaty, an investor in the Islamic center site.

"I am making this offer as a resident of New York and citizen of the United States, not because I think the location is a spectacular one (because it is not), but because it will end a very serious, inflammatory, and highly divisive situation that is destined, in my opinion, to only get worse," he wrote.

Rauf had said Wednesday evening that "nothing is off the table" when asked whether he would consider moving the site.

"We are consulting, talking to various people about how to do this so that we negotiate the best and safest option."

The imam told CNN's Soledad O'Brien on "Larry King Live" that "had I known [the controversy] would happen, we certainly would never have done this."

Asked if he meant he would not have picked the location, Rauf said, "we would not have done something that would create more divisiveness."

Earlier Thursday, Obama called the plan by Jones to burn the Qurans on Saturday a "recruitment bonanza for al Qaeda."

"You could have serious violence in places like Pakistan or Afghanistan" as a result of the burning, Obama said on ABC's "Good Morning America." "This could increase the recruitment of individuals who'd be willing to blow themselves up in American cities, or European cities."

Jones previously had said he would proceed with the plan Saturday despite increased pressure to abandon the proposal and warnings that going ahead could endanger U.S. troops and Americans worldwide.

Interpol on Thursday issued a global alert to its 188 member countries, warning of a "strong likelihood" of violent attacks if the Quran burning proceeded.

The FBI visited Jones at the Dove Center on Thursday, according to Jeffrey Westcott, special agent in charge of the Jacksonville, Florida, bureau. The FBI also visited him a few weeks ago, he said, but would not say what was discussed.

Earlier Thursday, discussions were taking place within the Obama administration about the possibility of intervening, White House spokesman Robert Gibbs told reporters.

Earlier this week, the top U.S. military commander in Afghanistan, Gen. David Petraeus, warned that the plan "could cause significant problems" for American troops overseas.

Jones had rejected the pleas, saying his message targets radical Islamists. "The general needs to point his finger to radical Islam and tell them to shut up, tell them to stop, tell them that we will not bow our knees to them," Jones said on CNN's "AC360." "We are burning the book. We are not killing someone. We are not murdering people."

Meanwhile, two websites associated with Jones and his church were down Thursday.

Rackspace Hosting took down the two sites because the church "violated the hate speech provision of our acceptable use policy," said spokesman Dan Goodgame.

The company investigated a complaint in the past couple of days and made the determination after reviewing both sites, said Goodgame, adding that Rackspace was under no pressure to act.

"This is not a constitutional issue. This is a contract issue," he said.

A Christian congregation in Germany, meanwhile, on Thursday distanced itself from Jones, its founder and former pastor. Stephan Baar, one of the leaders of the Christian Community of Cologne, said the congregation split with Jones in 2008 over differences in the way the church was run.

CNN's Paul Courson, Carol Cratty, Tristan Smith, Marylynn Ryan, Phil Gast and Rich Phillips contributed to this report.