A multi-racial group of US police unions had earlier called for Obama to apologise for for his prior statement on the arrrest.
"All of us collectively and individually believe he acted appropriately as any police officer would in conducting a response to a break-in in progress in processing and and disposing of the case"
Alan Macdonald, counsel for Cambridge police
Union leaders said on Friday that they believe Crowley acted correctly last week when he arrested Gates for disorderly conduct.
"I think the president should make an apology to all law enforcement personnel," said Steve Killian, the president of the Cambridge Police Patrol Officers Association.
Crowley did not speak about the arrest on Friday.
Crowley was sent to Gates' home last week after a woman called the police, saying that she had seen two men trying to force their way into his property.
But Gates, a professor at Harvard University, had only been having difficulty opening his front door.
Gates showed identification to Crowley to prove that he was the owner of the house when police arrived.
He is then alleged to have accused Crowley of racial profiling.
Crowley handcuffed Gates and took him to the local police station for 'processing' before Gates was later released without charge.
Speaking on Wednesday at a nationally televised press conference, Obama said that the officers who went to Gates' home had acted inappropriately, while admitting he was not in possession of all of the facts on the case.
"I think it's fair to say, number one, any of us would be pretty angry [to be arrested at one’s own home]" Obama said.
"Number two, that the Cambridge police acted stupidly in arresting somebody when there was already proof that they were in their own home.
“What I think we know separate and apart from this incident - is that there is a long history in this country of African-Americans and Latinos being stopped by law enforcement disproportionately, and that's just a fact."
Alan Macdonald, a counsel for Cambridge police, said the department believed that Crowley had not acted inappropriately in arresting Gates.
"All of us collectively and individually believe he acted appropriately as any police officer would in conducting a response to a break-in in progress, in processing and and disposing of the case," he said.
Robert C. Haas, the Cambrige police commissioner, has said the department is "deeply pained" by Obama's criticism, adding that he trusted Crowley's judgment.
Crowley has taught racial profiling to police officers for several years.