The US Justice Department has said it is looking into Trayvon Martin's death to determine whether federal prosecutors will file criminal civil rights charges against George Zimmerman.
The neighbourhood watch volunteer was found not guilty of the murder of Trayvon, an unarmed black teenager, in Florida last year.
The verdict has led to largely peaceful protests across the country by civil rights leaders and others.
Protests took place in New York as about 1,000 to 2,000 demonstrators crowded a few blocks around Times Square, chanting "no justice, no peace".
The rally started earlier in the day in Union Square with a couple dozen people, and then slowly grew into a gathering of thousands.
They abandoned their initial site to march in the streets towards Times Square, slowing or stopping traffic.
Police attempted to funnel the crowd into controlled lanes but were unable to.
A jury late Saturday found 29-year-old Mr Zimmerman not guilty of second-degree murder and declined to convict him on a lesser charge of manslaughter.
Mr Zimmerman has said he shot the 17-year-old in self-defence in a night-time confrontation in his Florida gated community, where Trayvon was visiting family.
Jurors were told that Mr Zimmerman was allowed to use deadly force when he shot the teen not only if he actually faced death or bodily harm, but also if he merely thought he did.
US President Barack Obama called Trayvon's death a tragedy for America but asked that everyone respect calls for calm reflection.