Patriarch Irinej has also been quoted as saying people should not "jump to conclusions ...before the truth can be determined."
It's understood there is no word yet on how the four blazes, one of which tore through St. Sava church in the Manhatten area of New York, started.
According to the Serbia-founded media organisation, B92, Patriarch Irinej told the Belgrade-based newspaper, Nedeljnik: "It is strange that four of our (Orthodox Christian) churches burned at the same time on three different continents.
"It's all symptomatic. We still don't know if it is some kind of warning, and what kind. And whether someone set them on fire in an organized way."
There is reportedly concern among some people in the Christian Orthodox community the blazes at St. Sava and in Australia and Russia may have been in retaliation for a recent move by Pope Francis to postpone the canonization of Croatian Cardinal Aloysius Stepinac.
The pontiff cancelled a ceremony for Stepinac, who was an infamous Nazi supporter, after Patriarch Irinej and the Serbian Orthodox Church urged him to reconsider.