Republican presidential candidate Herman Cain clarified his stance on appointing Muslims to government positions during CNN's New Hampshire GOP debate on Monday.

The former CEO of Godfather's Pizza had previously told ThinkProgress that he would not be comfortable appointing a Muslim to his White House cabinet or as a federal judge, because there was a "creeping attempt" to "ease Sharia law and the Muslim faith into our government."

"You have peaceful Muslims, then you have militant Muslims, those that are trying to kill us," Cain said Monday. "I was thinking about the ones that were trying to kill us."

He added that people who work for the government should be committed to the U.S. Constitution and would need to interview any Muslim before appointing them.

"It's not a litmus test," Cain said. "It's making sure we have people committed to the Constitution first in order for them to work effectively in the administration."