Republican presidential candidate Ben Carson said Islam isn't consistent with the U.S. Constitution and volunteered that a Muslim should not be president.

Mr. Carson’s comments, aired on NBC's "Meet the Press" on Sunday, came after host Chuck Todd asked if a president’s faith should matter. The question was in the context of Donald Trump on Thursday not correcting a New Hampshire town hall questioner who asserted President is Muslim and proposed “getting rid” of purported Muslim “training camps” in the U.S.

“It...