Davie, appointed to the role following the resignation of George Entwistle at the weekend, was being questioned by Dermot Murnaghan on his predecessor when he decided to end the interview early.
"As editor in chief you are responsible. What I'm saying is [Entwistle] has taken responsibility; these are questions for him," said Davie, while repeatedly glancing off camera.
"Anyway I will go now because I've got a lot to do; the BBC is taking action and that's what we're going to do. I've got a job and I'm going to get on with it, thank you Dermot."
Murnaghan tried to ask Davie whether more "heads will roll" following today's departures of senior news executives, but Davie declined to answer and just rather awkwardly walked out of shot.
However, the BBC Press Office later denied that Davie had 'walked off' the interview.
It tweeted: "DG did not walk off from his interview with Sky. Interview overran, clashing with other interviews."
Davie has promised to "get a grip" at the corporation following the resignation of Entwistle over a Newsnight report that led to a former Tory Treasurer wrongly being accused of child abuse.
In a letter to BBC staff today, he said that he was "determined to give the BBC the clarity and leadership it deserves in the next few weeks".
"You can expect to see management pulling together as one team, focused on tackling the problems the BBC currently faces head on," he said.
"But I also expect you to continue to make the programmes and services that our audiences love and that make the BBC unique."
Davie, who is to be the next chief executive of BBC Worldwide, said that a "clear line of command" has now been set up in news.
This includes director of news Helen Boaden and her deputy Steven Mitchell "stepping aside" pending completion of an internal review into the controversial dropping of a Newsnight investigation into sex abuse allegations against Jimmy Savile.
> BBC in crisis: Ofcom's Ed Richards tipped as new DG
> BBC's head of news Helen Boaden 'steps aside'
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