Proactiva Open Arms accuses Libyan coastguards of having saved the rest of the migrants on board the dinghy but not two women and the child, whom they say refused to board the rescue vessel and go back to Libya.
The NGO alleges that as a result, the coastguards left them and deflated the dinghy. Rescuers let air out of migrants' boats to stop them from being re-used and this boat had been slashed with a knife.
One of the women and the child, believed to be four years old, drowned, while the other woman was found alive and taken aboard the Open Arms vessel.
"We have filed a complaint against the captain of the (merchant ship) Triades for failing to help and for involuntary manslaughter and we'll also do it against the captain of the Libyan patrol," Oscar Camps, the Open Arms captain and founder of the NGO, said at a news conference after the rescue ship docked in Spain on Saturday, four days after the mission.
Libya's coast guard disputed the account on Tuesday but offered no explanation for how the three migrants came to be stranded on the remains of the dinghy.
The skipper of Tirades, the Panamanian-registered vessel which discovered the migrants at sea, could not be reached for comment on Saturday.
"We are indignant, we once again condemn the policies being followed in the central Mediterranean, not just by one government but by several. The difficulties we have faced to save one life are just incredible," Camps said.