B737-800
Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP)
Situational Awareness; Distraction
Conflict Airborne Conflict; Deviation - Altitude Excursion From Assigned Altitude; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Issued New Clearance; Flight Crew Requested ATC Assistance / Clarification; Flight Crew Took Evasive Action
Airspace Structure; Procedure
TCAS RA. On departure from ZZZ on Runway XX; we were given left turn to 149; climb 6;000 feet. In the turn; ATC said maintain 4;000 feet for traffic at 10 o'clock at 4;500 feet. As I went wings level; I could see the helicopter at 10 o'clock within a half mile of our current position. About 3;500 feet; we got a TA. I slowed my vertical speed as I approached 4;000 feet but upon capture; we got a RA telling us to 'monitor vertical speed.' The red line for the RA was on the horizon so I pitched just below the horizon. The First Officer informed ATC of the RA and that we were in a descent. ATC responded saying we were below the MVA (Minimum Vectoring Altitude) and to get back to 4;000 feet when able. At 3;600 feet; we were clear of conflict and climbed back to 4;000 feet. We continued the departure as normal. There wasn't much room for vectoring because of the mountains surrounding the valley. I believe the helicopter was VFR because of their altitude. ATC could have possibly kept us on the ground longer or given a delayed turn until helicopter was no longer a conflict.
TCAS RA on departure from ZZZ. Initially received climb via the ZZZZZ4 SID except maintain 5;000 feet. Prior to takeoff received amended clearance of left turn 149 climb 4;000 feet. ATC called traffic in the turn and we were looking. Nearing completion of turn and climb received TA followed by RA target 700 feet to 500 feet above and got the 'monitor vertical speed' we descended and made the standard  callouts to ATC. At 3;700 feet ATC warned of low altitude and below MVA (Minimum Vectoring Altitude). We were VMC and received the 'clear conflict' and climbed back to 4000 feet and continued the flight uneventfully.I think ATC knew about this target prior to takeoff and that's why they amended the clearance. I believe their hands were tied with a vector because of rising terrain and altitude separation due to Minimum Vectoring Altitude. We followed our training and everything worked out; would have been worse in IMC. Captain (Pilot Flying) says he saw helicopter but I couldn't see from First Officer seat in left turn.
Air carrier flight crew reported they responded to a TCAS/RA for a VFR helicopter by descending then were advised by ATC they were flying below the Minimum Vectoring Altitude.