'Gunshots to head'
Nicole Johnston, Al Jazeera's correspondent in Gaza, said there were six people on the boat when it came under Israeli fire.
"Four were killed, one escaped - a senior member of al-Aqsa - and one person is still missing. The group presumes he too is dead.
"The men were doing group training exercises, they were not fishing as had previously been reported by Palestinian medical sources that said they were fishermen," she said.
Moawiya Hassanain, a Palestinian health official, said two of the dead had suffered multiple gunshots to the head.
The incident came a week after nine pro-Palestinian activists were killedfollowing an Israeli raid on a Gaza-bound aid ship.
Israel has been enforcing a blockade of Gaza since 2007, when Hamas took control of the territory. The closure also includes a maritime blockade.