Pastor Terry Jones had threatened to burn the Muslim holy book on the anniversary of the Sept. 11 attacks over plans to build an Islamic center near where militants brought down the World Trade Center nine years ago.
He flew to New York and appeared on NBC's "Today" show.
He says that his church's goal was "to expose that there is an element of Islam that is very dangerous and very radical."
He told NBC that "we have definitely accomplished that mission."
He says no meeting is planned with the imam leading the center but he hopes one will take place.
Jones' Gainesville, Fla.-based church, the Dove World Outreach Center, had said it would hold an anti-Islamic demonstration on September 11, which they designated as "International Burn-a-Quran Day," in which church members would burn copies of the Holy Book. The announcement sparked denunciations and protests around the world, including warnings by U.S. officials, religious leaders, and military leaders, who warned such a demonstration could motivate anti-American violence and jeopardize U.S. forces.
President Obama referred to the planned book burning as a "stunt" that would endanger American lives.
Jones backtracked earlier this week, and renewed his assertions that his church would not burn holy books.
"Not today, not ever," he said on "Today." "We're not going to go back and do it. It is totally canceled. We would hope that through that, that will open up a door [to] be able to talk to the Imam about the 'Ground Zero mosque.'"
Jones arrived in new York City last night, hoping to meet with leaders of the Islamic center being planned several blocks north of Ground Zero.
Imam Feisal Abdul Rauf, leader of the planned center, said Friday that he was "prepared to consider meeting with anyone who is seriously committed to pursuing peace," but had no meeting planned with Jones.
"We have come here with the hopes of speaking with the Imam," Jones explained on "Today." "We feel that we have somewhat of a common denominator in the fact that most people do not want the mosque near Ground Zero, and of course I assume all Muslims do not want us to burn the Quran." .
He said there have been voice mails exchanged, but no meeting scheduled as of yet. "We have a couple of people who are working on it who are mediating."
When asked why he canceled the planned Quran burning, Jones said, "We feel that whenever we started this out, one of our reasons was to show, to expose that there is an element of Islam that is very dangerous and very radical. I believe that we have definitely accomplished that mission, even though we have not burned one Quran."
He said he has received death threats.
Jones likened his decision to pursue the plans to burn Qurans, and then cancel the event, with the Biblical story of Abraham. "Abraham was also called to do something very crazy, I mean God told him to go the mountain and sacrifice his son. Of course Abraham was much wiser than us, he told no one. So he got to the mountain. He started to do it, and God told him to stop.
"So we feel we have accomplished our goal," he said. "We're obedient. We feel that God is telling us to stop. And we also hope that with us making this first gesture, not burning the Quran - to say, 'No, we're not going to do it, not today, not ever. We're not going to go back and do it. It is totally canceled - we would hope that through that, maybe that will open up a door, [to] be able to talk to the Imam about the Ground Zero mosque."
He denied that he made the Quran-burning plans to court publicity.
"Absolutely not. We were 100% convinced that this was a type of a mission," he said. "I am of the opinion it is much larger than our politicians and our news media. . . . We have proved that point by the reaction worldwide."
More Coverage Marking the 9th Anniversary of 9/11:
Obama: 9/11 Victims Endure in Our Nation's Heart
President Obama Speaks at Pentagon Memorial
Biden Speaks on 9/11 at Ground Zero
Michelle Obama Remembers Flight 93
Laura Bush Speaks at Flight 93 Memorial
Islam Controversies Cast Shadow Over 9/11 Events
Proposed Islamic Center Divides 9/11 Families
NYC More Ready for Huge Disaster Than on 9/11?
Muslim Scholar: Don't Build Islamic Center
Obama Remembers Sept. 11, Calls for Unity
Rebuilding Ground Zero