NASHUA — State troopers from Massachusetts and New Hampshire were relieved of duty Thursday as authorities investigated their involvement in the violent arrest of a driver who led police on a lengthy high-speed chase.

A day after TV news footage showed at least two police officers pummeling a suspect who had dropped to his knees and surrendered, one trooper from each state was taken off the job, and the head of the Massachusetts State Police said the officers’ use of force was disturbing.

“The Massachusetts State Police expect and demand all department members to act at all times with integrity, honor, and adherence to the law,’’ Colonel Richard McKeon said in a statement. “If it is determined that a department member has not lived up to those expectations, we will take appropriate action.’’

Colonel Robert Quinn, director of the New Hampshire State Police, said the trooper involved in the arrest was immediately relieved from duty.

“I want the public and law enforcement personnel to know that the Division of State Police does not condone the unjustified use of force and it will not be tolerated,’’ Quinn said at an afternoon news conference. “The core values of our state troopers are fairness, professionalism, and integrity.’’

The troopers were not identified. An internal hearing for the Massachusetts trooper is slated for Friday. The investigation will seek to determine whether policies “governing the use of force’’ were followed, McKeon said.

“If that investigation determines that departmental violations occurred, we will take appropriate and commensurate disciplinary action,’’ he said, which could include suspension.

At a time of intense public scrutiny of police misconduct nationally, McKeon asked the public to “recognize that the alleged actions of one member do not reflect on the rest of the department.’’

The New Hampshire attorney general’s office has launched a criminal investigation into the circumstances of the arrest, a burst of violence that followed a protracted chase from Central Massachusetts to a residential street in Nashua.

The suspect, Richard Simone, 50, of Worcester, was wanted on assault charges stemming from an incident Sunday in Millbury, in which he led police on an early-morning chase and “intentionally swerved his vehicle’’ at an officer, according to a Millbury police spokeswoman.

On Wednesday afternoon, Holden police tried to pull Simone over, but he failed to stop, authorities said, sparking the pursuit.

Simone appeared in a Nashua courtroom Thursday on a fugitive-from-justice charge, and did not contest his extradition to Massachusetts. The chase and his arrest were not discussed in court.

After a private conversation with Simone’s lawyer, Judge James Leary said Simone is “going to be seeking some medical attention’’ but did not provide details.

Leary then asked Simone’s lawyer, Pamela Jones, whether Simone had a “clear enough’’ mind to waive extradition.

“I do believe he’s in a clear enough mind, but I do have concerns about his well-being,’’ Jones said.

Simone answered “Yes, sir,’’ when Leary asked whether he understood the process of extradition.

In Massachusetts, Simone will be charged with assault and battery with a dangerous weapon, failing to stop for police, and violating his probation related to other cases. Authorities said they did not know when he would be arraigned on the charges.

McKeon, the head of the Massachusetts State Police, said the investigation will also determine whether officers adhered to the department’s “rigorous pursuit policy.’’

In the footage shot by media helicopters overhead, Simone is shown slowly getting out of a pickup truck, as officers close in with guns drawn. When Simone drops to his knees, the officers rush toward him, and at least two are seen punching him repeatedly.

In a statement, Governor Maggie Hassan of New Hampshire said the footage of the arrest “raises serious concerns.’’

“All New Hampshire public safety officials are held to the highest standards, and it is important and appropriate that the attorney general’s office has opened an investigation into the incident,’’ she said. “We must treat this incident with the utmost seriousness without disparaging all of the hard-working police officers who put their lives on the line every day to keep us safe.’’

Police say Simone fled police onto Interstate 190 northbound, then Route 117 in Lancaster. He later continued onto Route 2 in Leominster and Interstate 495 northbound in Littleton, making abrupt lane changes to evade capture.

Simone then sped into Hudson, N.H., where local police and New Hampshire troopers joined the chase, police said. He was involved in a crash near the town hall, but continued into Nashua, where he finally came to a stop.

Kathy McCabe can be reached at Katherine.McCabe@globe.com. Follow her on Twitter @GlobeKMcCabe. Andy Rosen can be reached at andrew.rosen@globe.com. Follow him on Twitter at @andyrosen.