Three churches in the capital Santiago were damaged by firebombs. Some flyers left behind warned that the next one was for the Pope.
But at another church south of the capital, a pamphlet used a phrase that refers to activism in the indigenous Mapuche territory.
President Michelle Bachelet described the incidents as "very strange".
"In a democracy, people can express themselves as long as they do it in a peaceful way," she told a radio station on Friday, adding that the attacks could not yet be tied to a particular group.