I agree with Mike. Pigeon or dove.
Since red-tailed hawks (including the famous Pale Male and Lola and their offspring) have made a comeback in New York City, they are helping to control the pigeon population. I understand that the city has also stopped using rat poison so the hawks can safely eat their fill.
We also have smaller hawks. Two merlins (sparrow hawks) hunt from the railing on my terrace. They wait for an unsuspecting finch or sparrow to fly by, then gang up on it, catching it in midair and shaking it to break its neck -- all very fast and clean. Sometimes they dump the body in one of my planters and come back for it later. It's always gone in a few hours; maybe they take it back to their nest to feed the youngsters.
I've stopped putting bird feeders on the terrace; they're like a free buffet for the hawks. Here are a few of our NYC "locals," photographed by Lincoln Karim, who maintains the web site.