The al-Jazeera satellite channel reported by telephone from the Turkish ship leading the flotilla that Israeli navy forces fired at the ship and boarded it, wounding the captain. The Turkish NTV network also reported an Israeli takeover with gunfire, and at least two people were killed.
The al-Jazeera broadcast ended with a voice shouting in Hebrew, "Everybody shut up!"
The television network said two activists had been killed and some 50 wounded. Organisers of the aid convoy said they were no longer in contact with the boats. The Israeli military have refused to comment.
The reports came just after daybreak, with the flotilla still well away from the Gaza shore. Israel had declared it would not allow the ships to reach Gaza.
In Turkey, news of the interception prompted protestors to attempt to storm the Israeli consulate in Istanbul in retaliation.
On Sunday, Huwaida Arraf, one of the organisers, said the six-ship flotilla began the journey from international waters off the coast of Cyprus on Sunday afternoon after two days of delays. She said they expected to reach Gaza, about 250 miles away, on Monday afternoon, and that two more ships would follow in "a second wave."
The flotilla was "fully prepared for the different scenarios" that might arise, and organizers were hopeful that Israeli authorities would "do what's right" and not stop the convoy, she said.
"We fully intend to go to Gaza regardless of any intimidation or threats of violence against us," she said. "They are going to have to forcefully stop us."