Excuse the slight paraphrasing:
Imam Feisal Rauf: "This is a deliberate attempt to present what I see as the real face of Islam to a city where some - since the terror attacks of 11 September, 2001 - have come to distrust the religion. This space [Ground Zero] has very powerful symbolism in the perception of the world. It is important for us to be stakeholders in what this symbolism means. What better place to show that we, as Muslims, condemn the acts of 9/11 than making this stand and making this statement here. When we say it here, we will be heard."
Mike Burke (whose fireman brother was killed 9/11): "Families of 9/11 victims do not want a mosque by Ground Zero. It is not Islamaphobia. It's just that me and others do not want an Islamic institution nearby. I think the first concern for the families is that the religious beliefs of the terrorists who struck is going to have such a prominent place right around the corner from Ground Zero. This is not an anti-Muslim effort. It is understandably… emotional for them to be suddenly told that around the corner from where their loved ones were killed they're going to put a mosque."
It's worth reading the short article which tees up the controversy pretty concisely and fairly.
Is this plan to build a landmark Islamic cultural centre two blocks from the Gound Zero site an inspired idea or a misstep?.