The barrage of lead weights damaged a helicopter that the activists had used earlier in the day to document the vessels' activities, Aslan said.
Activists on the ship also heard shots being fired and the Coast Guard in the Mediterranean port of Iskenderun was called to intervene, she said.
No one answered telephone calls at a company in the Black Sea town of Giresun whose vessel Greenpeace said was involved in the attack.
The head of a main bluefin tuna fishing company in the Mediterranean, Ak Tuna Balikcilik, was at sea and could not be reached for comment, a company secretary said. It was not clear if any of that company's vessels were involved in the incident.
The Arctic Sunrise was sailing between Turkey and Cyprus to draw attention to overfishing at a channel that Greenpeace says is a main breeding area for bluefin tuna.
Greenpeace wants Turkey to immediately stop issuing bluefin tuna fishing permits in the channel and to declare the area a marine reserve.
"We understand that these guys are angry and we're angry too," Greenpeace representative Karli Thomas said. "But the real problem here is being caused by the refusal of governments to take action to regulate a fishery that's fishing itself to death."
"The population of tuna is close to extinction," Thomas said. "If we don't protect the breeding and spawning grounds now, there will be no fish for the future."
Atlantic bluefin tuna stocks are under serious threat from overfishing. The European Union last year called for stronger protection of the bluefin tuna by extending the fishing offseason, reducing black market fishing and imposing new worldwide cuts in catch quotas.
The vast majority of Atlantic bluefin tuna is caught in the eastern Atlantic and Mediterranean, with a smaller percentage fished in the western Atlantic.
The Turkish vessels fish in the Black Sea and the Sea of Marmara in the winter and move to the Mediterranean to hunt bluefin tuna there in the summer.