Air carrier Captain reported a NMAC with a helicopter while on visual approach. Flight crew responded to the TCAS alert and continued the approach.

Narrative

While we were flying the river visual to Runway 19 into DCA we received a TCAS alert. We were around SETOC or just past it and fully configured to land. There was; what I could only guess as I never saw it; a helicopter about 300ft below us. The TCAS showed it climbing but at a very very slow rate as it never showed closer than 300ft to us. When we flew over top of it; we got a monitor vertical speed alert from TCAS which we then pitched into the green arc on the VSI which was -300fpm or greater. After we received the "clear of conflict" the FO corrected and got back on glide path. I assessed that we were still within stable approach criteria and we continued the approach and landed in DCA without further issue. We never received a warning of the traffic from ATC so we were unaware it was there.Suggestion: Need to have better separation for DCA traffic on the river visual to the helicopter traffic that is flying up and down the river. Maybe by timing the separation of when we began the approach to where that traffic will be when we cross overhead."