Luke Jones, the son of the Rev. Terry Jones, told reporters Friday that the event will not take place Saturday. But he says he can't speak about whether there will be a future event.
The pastor called off the Quran-burning event after claiming he had commitments from Muslim leaders that a mosque would not be built near ground zero in New York. When that was met with denials, the minister said the burning event was suspended.
The pastor says he will to fly to New York to meet with the imam overseeing the mosque project there.
However, Imam Feisal Abdul Rauf said Friday that he has no plans to meet Saturday.
"I am prepared to consider meeting with anyone who is seriously committed to pursuing peace," Imam Feisal Abdul Rauf said in a prepared statement. "We have no such meeting planned at this time. Our plans for the community center have not changed. With the solemn day of September 11 upon us, I encourage everyone to take time for prayer and reflection."
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The statement appeared to leave open the possibility of a meeting but did not mention Jones by name or say specifically whether Rauf believed the pastor was a peacemaker who deserved a meeting.
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Jones created outrage in the U.S. and around the world by threatening to have his small congregation burn the Quran.
The anti-Islamic pastor of the Dove World Outreach Center in Gainesville, Fla., had said Thursday that he would back off his plans for the Quran-burning based conversations with a Florida imam who, Jones said, offered to have the New York project moved.
Then Jones reversed course and lashed out at the local imam, Muhammad Musri of the Islamic Society of Central Florida. No firm deal to move the New York Islamic center ever existed.
Jones' daughter, Emma, said in an interview with the German news website Spiegel Online that she begged him in an e-mail, "Papa, don't do it," but he didn't answer. She said she hasn't had contact with him since 2008, when he was ousted by members of a church he had founded in Cologne, Germany.