Man fatally shot outside his Brooklyn apartment building

A Brooklyn man was gunned down outside his apartment building Tuesday — and a suspected gunman was in custody, police and sources said.

The 26-year-old victim was shot outside the Brownsville Houses at 350 Blake Ave. near Mother Gaston Blvd. at 9:13 p.m. and then staggered up to the fourth floor inside the complex, where he collapsed, a source said.

Nearby officers responding to the shooting, however, managed to chase down the suspected assailant around the corner on Dumont Ave. at Rockaway Ave., the source said. A gun was also recovered.

The victim was rushed to Brookdale Hospital but he could not be saved, cops said.

Neither the name of the victim or shooter were immediately released.