"This is an issue people are going to come to with strongly held convictions," Burton told reporters aboard Air Force One, as Obama flew to an appearance in Seattle. "He's happy our thriving democracy is continuing to produce vigorous debate."
On Monday, Reid called for the $100 million mosque to be built someplace else. His opinion made him the highest profile Democrat to oppose the plan, which locates the mosque two blocks from the site of the Sept. 11 terrorist attacks.
"That includes the right to build a place of worship and a community center on private property in lower Manhattan, in accordance with local laws and ordinances," said the president.
However, Obama backtracked a day later, saying that wasn't an endorsement of the specific mosque plan.
Burton told reporters that Obama "respects the right of anybody... to disagree with his opinion on this."
Many Republicans have portrayed Obama as out of touch with Americans' feelings on the issue, and some Democrats have said they wish he hadn't weighed in.
However, Burton said Obama didn't consider the politics of his remarks, and felt he had to speak out in defense of key constitutional values.
Meantime, New York Gov. David Paterson has suggested that the mosque be built at a different location than near Ground Zero. Paterson's office announced on Tuesday that the governor will meet soon with the mosque's developers.
The Associated Press contributed to this report.