Police Commissioner William Bratton said officers were giving protesters "breathing room."
"As long as they remain nonviolent and as long as they don't engage in issues that cause fear or create vandalism, we will work with them to allow them to demonstrate," he said.
Protests were mostly peaceful, with just two arrests, including that of a man who threw a jar of fake blood that struck Bratton. Police said protesters briefly shut down the Brooklyn Bridge and one of the three spans of the Robert F. Kennedy Bridge, formerly known as the Triborough Bridge, on Tuesday night.
Protesters also marched in Seattle, Washington, and Albuquerque, New Mexico, and disrupted traffic in St. Louis and Cleveland. Rallies were held in Michigan, Maine, Georgia, Wisconsin and other states.
United Nations Secretary General Ban Ki-moon on Tuesday urged protesters in Ferguson and elsewhere in the United States to refrain from violence and called on law enforcement to protect the rights of people to demonstrate peacefully.
Protesters disrupted traffic for several hours in St. Louis by blocking major intersections, an interstate highway and a Mississippi River bridge connecting the city to Illinois. About 300 people marched to the St. Louis courthouse, chanting "You didn't indict. We shall fight." Police used pepper spray and arrested several demonstrators who blocked major intersections in the city.
Riot police arrested several demonstrators who sat in the middle of an interstate highway. They used pepper spray to disperse the crowd.
In Philadelphia, where hundreds marched, protester Ethan Jury said, "Mike Brown is an emblem [of a movement]. This country is at its boiling point ... How many people need to die? How many black people need to die?"
A rally in Minneapolis turned violent when a car struck a protester and then burst through a pack of others who surrounded it. A woman suffered minor injuries. Several hundred people had gathered Tuesday afternoon near the 3rd Precinct police outpost to show solidarity with Brown. The driver called police soon afterward to report the incident, and police spokesman John Elder said it was under investigation.
In Boston protesters marched past a correctional facility, where inmates taped Brown's name on a window in solidarity with the marchers outside. The Boston Globe estimated 1,400 people marched through Back Bay and the financial district. An altercation between protesters and police outside South Station resulted in about a dozen protesters placed in restraints, the paper reported.
Several hundred people from historically black schools Morehouse College and Clark Atlanta University in Georgia held peaceful demonstrations. But as the night wore on, some groups split off and tried to block a freeway, and police said some windows were broken.