"To Pastor Jones and those who want to build a mosque," Boehner said, "just because you have a right to do something in America, does not mean it is the right thing to do."
Rauf told Amanpour that burning Korans and building his center near Ground Zero are nothing alike.
"You can't equate the two," he said. "This is now the moment between the radicals and the moderates. We are to look at it from the point of view of those who are trying to create a breakthrough for moderation against those who are trying to create a breakthrough for the radical voices. How can you equate burning of any person's scripture with an attempt to build interfaith dialogue? This is a house with multifaith stakeholders, with multifaith partners intended to work together towards building peace."
In his Times op-ed article, Rauf argued that, despite comments from critics such as Boehner, building the project that he described Wednesday as an interfaith center called Cordoba House is the right thing to do.
"Our initiative is intended to cultivate understanding among all religions and cultures," he wrote. "Our broader mission -- to strengthen relations between the Western and Muslim worlds and to help counter radical ideology -- lies not in skirting the margins of issues that have polarized relations within the Muslim world and between non-Muslims and Muslims. It lies in confronting them as a joint multifaith, multinational effort.
"From the political conflicts between Israelis and Palestinians to the building of a community center in Lower Manhattan, Muslims and members of all faiths must work together if we are ever going to succeed in fostering understanding and peace," he wrote.
However, plans for the "Ground Zero mosque," approved by the city of New York, have stirred opposition from critics who claim that it is insensitive to build what until recently had been presented as an Islamic center so close to what many consider hallowed ground attacked by Islamic extremists.
Opponents have ranged from the Anti-Defamation League to conservative politicians like Sarah Palin and Newt Gingrich. New York Gov. David Paterson, a Democrat, was rebuffed when he offered to help Rauf find another site.
Rauf, a long-time imam at a mosque a dozen blocks from Ground Zero, said he didn't make his arguments earlier because he wanted to be on American soil before he spoke. He had been on a State Department-sponsored goodwill tour of the Middle East until recently.
"I'm proud to be American," Rauf told ABC News on Aug. 31, just before returning home. "America is where I found my faith."
The imam told ABC News that the battle over the project "has expanded beyond a piece of real estate and expanded to Islam in America and what it means for America."
On CNN, as he has done previously, Rauf suggested that conservative politicians were using the issue to stoke support in the months before the November elections.
"This story first broke last December in the New York Times and nobody objected," he told CNN. "This controversy only began in May. And it began as a result of some politicians who decided to use this for certain political purposes."