According to the coast guard, both vessels ignored warnings to stop and attempted to ram the coast guard's patrol ships late on Thursday night. They were both stopped eventually with shots fired on their outboard motors.
One of the boats was carrying 20 migrants and two of the alleged traffickers, while the other had 17 migrants and another suspected trafficker on board.
Kos is in very close proximity to the Turkish coast, from which vessels attempt to cross the Aegean waters carrying migrants to reach Greek islands or the mainland.
This latest incident comes on the back of another successful swoop on traffickers by Greek authorities on the northern land border with Turkey.
Last Friday Greek police said they had smashed a criminal gang that smuggled migrants packed into trucks across the border with Turkey for up to 4,000 euros each. Police said that so far seven suspects have been arrested on charges of forming a criminal gang, while at least 20 more have been identified. (ANSAmed).