He said the second soldier to land opened fire after being shot in the stomach.
"He simply pulled out his gun and shot the shooter," Ashkenazi said.
No guns were found aboard the ship but the military has previously said that activists seized at least one firearm from the soldiers during the clashes and that it found evidence of a gun not used by Israeli soldiers.
Ashkenazi rejected Turkish charges that some of the dead had been shot "execution-style" at point-blank range, saying that shots had been fired at close range as part of a life or death struggle.
"There was an instance when a soldier was being attacked with an axe," he said.
"Somebody with an axe ... that is life-threatening."
Al Jazeera's Jacky Rowland, reporting from Jerusalem, said Ashkenazi was the first official to give an apparently detailed explanation of what happened on the vessel on May 31.
"He has given us the greatest details that we have had so far about the events on board the [Turkish-flagged] Mavi Marmara.
"He had all these video aids as well, films, graphics taking the commission through blow-by-blow of the events of the early morning - from the final radio warnings to the actual minute-by-minute attack on the ship," she said.
"He did make a few criticisms, not only of the operation, but crucially of the period leading up to the information. In particular, he isolated intelligence failings and their lack of detail about the Turkish group, the IHH, that organised this convoy.
"There was an implicit suggestion there that maybe that was because the Turks, themselves, hadn't provided a lot of information. That was not something he wanted to pursue in open court. He said he'd talk more about Turkey behind closed doors.
"On the operation itself, Ashkenazi said that in retrospect he would have gone in with more force, more ropes and more soldiers to calm the situation on the deck right at the very beginning."
Israel has always insisted its commandos resorted to force after they were attacked on the deck of the Mavi Marmara, but activists on board say the soldiers opened fire as soon as they landed.
Ashkenazi was the third senior figure to address the inquiry this week after Binyamin Netanyahu, the Israeli prime minister, and Ehud Barak, the defence minister.
The commission offers a closely-managed forum where Israeli leaders can argue their case. Its summary and that of a military investigation are due to be sent to an independent investigation which opened at the United Nations in New York on Tuesday.