Mayor Bill de Blasio texted Blake after the two men missed each other's calls, said Karen Hinton, a spokeswoman for the mayor.
De Blasio apologized to Blake and planned to call him later Friday, according to Hinton.
Blake, 35, spent five or 10 minutes with his hands cuffed behind his back before police realized they had the wrong guy and let him go, Bratton said at a news conference Thursday.
Bratton said the incident "should not have happened" but insisted Blake -- who is biracial -- wasn't detained because of race.
"I don't believe that race was a factor," Bratton said. "This rush to put a race tag on it, I'm sorry, that's not involved in this at all."
An undercover officer involved in the incident outside the Grand Hyatt Hotel has been placed on desk duty, Bratton has said.
In a statement, Patrick Lynch, president of the police union, said, "We agree with the police commissioner that the first story is never the whole story and believe that placing this officer on modified duty is premature and unwarranted. No police officer should ever face punitive action before a complete review of the facts."
The officer, James Frascatore, who is white, is a defendant in two federal lawsuits filed earlier that allege excessive force in separate incidents.
Last year, Frascatore was named in an amended complaint filed in federal court in Brooklyn alleging he and seven other officers and sergeants beat and unlawfully arrested a man in a Queens deli in May 2013.
The officer is also named in a complaint filed in May alleging that officers used excessive force against a man named Warren Diggs for riding his bicycle on the sidewalk in 2013. The city denies the allegations in an answer to the complaint, according to court paperwork.
Officers investigating fraud case
Reacting to Wednesday's incident, Blake, once ranked No. 4 in the world, told the Daily News
that "in my mind there's probably a race factor involved, but no matter what, there's no reason for anybody to do that to anybody. ... I was just standing there. I wasn't running. It's not even close (to being OK). It's blatantly unnecessary."
Detectives from the Identity Theft Task Force went to the hotel to arrest people purchasing high-end shoes with fraudulent credit cards, said Robert Boyce, chief of detectives for the New York police.
Officers set up the sting after a company that delivered goods on demand notified police that a group had purchased $18,000 in items using fraudulent credit cards, Boyce said.
At the hotel, a courier delivered the goods to one man and police arrested him, Boyce said, identifying the suspect as a white male from England visiting the United States on a student visa.
"That courier then told the owner of the service provider that the individual standing 8 feet away, Mr. James Blake, was the other perpetrator" in the earlier incident, Boyce said.
Officers also identified Blake as a suspect from a photo from the company supplying the goods, Boyce said.
The company got the photo off Instagram based on the name of a person they'd done business with, he said.
"If you look at the photo ... it's a reasonable likeness to Mr. Blake," Boyce said. "They look like twins."
But the Instagram photo can't be shown to the press, he said, because it turned out to be the image of an innocent person, not anybody involved in the fraud case.
Blake was let go shortly after a retired New York police officer informed detectives he was a tennis player.
Police went inside the hotel and arrested a second suspect, also a Briton, Boyce said.
The men -- identified as Jarmaine Grey, 26, and James Short, 27 -- were charged with identity theft and credit card fraud, authorities said.
The suspects allegedly used fraudulent American Express cards to purchase more than $8,000 worth of goods, including champagne, Louis Vuitton bags and iPhones, according to the Manhattan district attorney's office. They were arraigned Thursday, with bail for both set at $50,000.
An attorney for Grey declined to comment. CNN has not heard back from Short's attorney.
Did police use too much force?
Bratton has ordered an internal investigation of the Blake incident. He wants to know how the mistake was made, if excessive force was used and why detention protocols were not followed.
He said the officers didn't report the incident to superiors, and he was unaware of it until Blake's comments hit the media.
"Was the force used inappropriate? The initial review is we believe it may not have been," he said.
Bratton said he's heard reports one of the officers did not display a badge. That may have been because he was undercover, Bratton said.
Blake, a former Olympian, told "Good Morning America" that he initially thought a friend was running toward him to try to surprise him with a bear hug.
Instead, "he picked me up and body-slammed me and put me on the ground and told me to turn over and shut my mouth, and put the cuffs on me," Blake told ABC.
He said he cooperated and tried to explain who he was and provide his identification but that his explanations were ignored.
"I'm shaken up," Blake said Thursday on "Good Morning America." "A couple bumps and bruises, but all right."
Blake also can take solace in the support he's received around the tennis world.
One of the women's game's all-time greats, Martina Navratilova, took to Twitter to call the situation "unacceptable" and "just outrageous."
And the sport's governing body stateside, the U.S. Tennis Association, said in a statement Thursday it is "deeply concerned about this troubling incident."
"James is the embodiment of a model citizen whose triumphs on and off the court continue to inspire tennis fans and nonfans alike," the USTA said. "We will continue to offer our support to James in any way we can as this investigation unfolds."