Bush was addressing ambassadors from Muslim states who attended the White House’s regular hosting of iftaar (Ramadan breaking-of-the-fast dinner).
Several Muslim-American leaders, who were not invited, protested outside the gates by holding their own iftaar ceremony and rally.
CAIR, America's largest Islamic civil liberties group, called the White House event "window dressing".
The Muslim American Society criticised Bush for not reassigning Lt Gen William Boykin for his anti-Muslim remarks. Society spokesman Raiid Tayih said Bush might be going easy on Boykin for fear of "upsetting his religious (Christian) right base".
Boykin, an evangelical Christian, sparked an international uproar by giving speeches while in uniform, referring to the so-called US war on terrorism as a battle with "Satan" as the enemy, and saying Muslims wanted to destroy America "because we're a Christian nation".
Bush told the ambassadors and other Muslim leaders at the iftaar that “we honour and welcome and value the Muslim faith” adding that “America rejects all forms of ethnic and religious bigotry... And we will always protect the most basic human freedom - the freedom to worship God without fear."
Before the iftaar, Bush told a news conference that remarks by Boykin, the deputy undersecretary of defence for intelligence, did not "reflect my point of view or the view of this administration".
However, the president did not comment directly on Boykin's statements or condemn his remarks, deferring to the Defence Department's inspector general, whose office is investigating his speeches at churches and prayer breakfasts.
In one speech, Boykin referred to a Muslim fighter in Somalia who said US forces would not catch him because Allah protected him. "Well, you know what I knew, that my God was bigger than his. I knew that my God was a real God, and his was an idol," Boykin said.
His comments prompted calls for Boykin to be reassigned.
"There are strong forces inside the administration and outside...seeking to marginalise the American Muslim community and unfortunately those voices are being listened to"
CAIR, in a statement said: "President Bush and Secretary Rumsfeld should also take this opportunity to further distance themselves from those who actively promote the clash of civilisations and religions.”
A top Pentagon aide said there were no plans to oust Boykin from his job.
Several Muslim-American groups criticised Bush's handling of the controversy.
"There are strong forces inside the administration and outside the administration seeking to marginalise the American-Muslim community and unfortunately those voices are being listened to," said CAIR spokesman Ibrahim Hooper.