At least three police officers are dead and seven others have been injured after two snipers opened fire during a protest over recent fatal police shootings in the US.

The gunfire broke out around 8.45pm on Thursday in Dallas while hundreds of people were gathered to protest shootings of black men in Louisiana and Minnesota.

A statement from Dallas Police Chief David Brown said three officers were deceased, two are in surgery and three are in critical condition.

"It appears that two snipers shot ten police officers from elevated positions during the protest/rally," the statement said.

Live TV video showed protesters marching along a street in downtown when the shots erupted and the crowd scattered, seeking cover.

Meanwhile, the Dallas Area Rapid Transit tweeted that it had lost a transit officer and three others had been injured.

The protesters gathered after a Minnesota officer on Wednesday fatally shot Philando Castile while he was in a car with a woman and a child in a St. Paul suburb.

The aftermath of the shooting was purportedly livestreamed in a widely shared Facebook video.

A day earlier, Alton Sterling was shot in Louisiana after being pinned to the pavement by two white officers. That, too, was captured on a cellphone video.

Video footage from the scene showed that protesters were marching along a street in downtown, about a kilometre from City Hall, when the shots erupted.

Texas Govenor Greg Abbott released a statement saying he has directed the Texas Department of Public Safety director to offer "whatever assistance the City of Dallas needs at this time".

"In times like this we must remember - and emphasise - the importance of uniting as Americans," he said.

The search for the gunman stretched throughout downtown Dallas, an area of hotels, restaurants, businesses and some residential apartments.

The scene was chaotic, with helicopters hovering overhead and officers with automatic rifles on the street corners.

"Everyone just started running," Devante Odom, 21, told The Dallas Morning News. "We lost touch with two of our friends just trying to get out of there."

Carlos Harris, who lives downtown told the newspaper that the shooters "were strategic. It was tap tap pause. Tap tap pause."

The gunshots in Dallas came amid protests nationwide over the recent police shootings.

In midtown Manhattan, protesters first gathered in Union Square Park where they chanted "The people united, never be divided!" and "What do we want? Justice. When do we want it? Now!"

A group of protesters then left the park and began marching up Fifth Avenue blocking traffic during the height of rush hour as police scrambled to keep up. Another group headed through Herald Square and Times Square where several arrests were reported.