David Dao

Already, attorneys have filed a chancery motion asking that all evidence in the case be preserved. David Dao's attorney, Thomas Demetrio, would not provide a timeline for filing the lawsuit other than to say he had two years to do so, and "I promise you it won't be that long."

"If you're going to eject a passenger, under no circumstances can it be done with unreasonable force or violence. That's the law," he said. "For a long time, airlines -- United, in particular -- have bullied us. ... We want respect and we want dignity. That's it. Not a big deal."

David Dao was filmed being dragged off the overbooked flight at Chicago O'Hare airport, bloodied and screaming, in a video watched millions of times online.

United Airlines said it would refund the ticket costs of all passengers on Sunday's flight.

The airline's chief executive, Oscar Munoz, is insisting he will not resign.

As of Tuesday, Dr Dao was still recovering in a Chicago hospital, his lawyer said, but a family member is expected to give a news conference on Thursday.