The bus, one of six carrying students from Farmingdale High School on Long Island, veered off Interstate 84 and rolled over Thursday in the center median in the town of Wawayanda, around 45 miles northwest of New York City.
Two adults died, and other passengers were seriously injured.
Paul Defendini, superintendent of Farmingdale schools, said in a statement Saturday that some of the injured students were still struggling, but all are expected to recover.
"I know that they appreciate all the well-wishes you are sending, and we can’t wait to welcome them back when they are ready to return," Defendini said.
The bus that crashed was carrying 40 students and four adults to a band camp in Greeley, Pennsylvania, about a 30-minute drive from the accident site.
It wasn't immediately clear Sunday how many people remained in area hospitals or what their conditions were. Messages were left with state and local officials.
State police said Saturday five passengers remained in critical condition. A total of 16 students and two adults were hospitalized Friday.
The two adults who died were band director Gina Pellettiere, 43, of Massapequa, and Beatrice Ferrari, 77, of Farmingdale, a retired teacher who was serving as a chaperone on the trip.
The National Transportation Safety Board is investigating the crash, seeking to prevent similar accidents, officials said.
Gov. Kathy Hochul said Thursday tire failure may have been to blame, but the NTSB said it was premature to speculate.
Associated Press wire services helped contribute to this report.