Savile, a popular television and radio personality, died in October 2011 at the age of 84. He has since been accused by numerous women of sexually abusing them when they were young teens.
Police are investigating the matter and say Savile may have assaulted as many as 200 girls, some in his BBC studio dressing room, hospitals or boarding schools, in five decades. The allegations came to light this month when ITV ran interviews with some of the alleged victims.
The New York Times quoted Entwistle as telling the parliamentary panel Tuesday the BBC is not trying to "avoid answering questions" from authorities in the official case.
He also said internal BBC investigations -- one into the broader culture of the company in decades past, the other into why a 2011 Newsnight program about the allegations against Savile was quashed -- were "the opposite of an attempt to hide things," the Times reported.
"There is no question in my mind that this is a very grave matter indeed," Entwistle said, insisting the institution had "done what it should have done."