The commissioner said the younger brother had been photographed at Times Square in 2012.
Mr. Bloomberg said city officials were told Wednesday night by the FBI that New York was next on the list of targets.
Meanwhile, Anzor Tsarnaev, father of the brothers, told reporters in Makhachkala, the capital of Russia’s Dagestan region, that he intended to travel to the U.S. to bury his older son.
“I am going to the United States. I want to say that I am going there to see my son, to bury the older one,” he said. “I don’t have any bad intentions. I don’t plan to blow up anything,”
Tamerlan Tsarnaev’s body remains in the custody of the Massachusetts chief medical examiner. The cause of death has yet to be determined.
Thirty-three of those injured in Boston remained hospitalized, one of them in critical condition. At least 14 people underwent amputations because of the blasts.