Police in New York have shot and killed a man who pulled out a knife and led them on a chase through Times Square.

The confrontation began Saturday afternoon in what is one of the most popular tourist areas of New York City.

Police say they stopped a 51-year-old man who appeared to be smoking marijuana near West 44th Street and Seventh Avenue, in the heart of Times Square.

The man then became agitated, pulling out a 28-centimetre knife and beginning to put a bandanna on his head, according to police.

He repeatedly ignored orders to drop the weapon and began backing down the avenue, continuing for a number of blocks and drawing many officers into a pursuit.

Investigators are looking into the situation.