Yes or "extremely sorry".
In House of Cards, an American TV drama, a dog was killed by a car. And the driver run away.
The owner of the dog and his friend Frank saw the dead dog. Frank said, "I am awfully sorry".
I think "awfully" stresses the unpleasant feeling, comparing "very" if Frank said, "I am very sorry". Am I right?
I mean "awfully" sounds stronger than "very". Am I correct?