EMB-170/175 Captain reported becoming distracted by reported traffic and losing command of the RNAV RNP approach sequence. The conditions were VMC. The crew then asked for and was given a visual approach by ATC. Later the pilots realized they had busted the Minimum Vector Altitude.

Narrative

Flying into ZZZ we were cleared for the RNAV Runway XXL. I was the pilot flying (PF) and having been cleared for the approach I armed approach mode and set the final approach fix altitude. Passing ZZZZZ the (IAP) the approach mode was active with RNP .30 and the aircraft was tracking the approach properly. As we approached ZZZZZ1 there was a yellow TCAS target to the North of our position and we had heard a C172 that had been cleared for the visual straight in. The First Officer (FO) was searching for the traffic but was unable to spot them; since the target was to our left and we were in VMC conditions I started searching outside as well. I had the LOC in the preview in case of an engine failure during missed approach to help navigate per company page XX-XX-XX. After passing ZZZZZ1 while searching for traffic I noticed the aircraft had not started the turn towards ZZZZZ2 and I saw then that the GPS approach was no longer active and the FMS had sequenced to green needles. I discontinued the approach and deselected approach mode; selected heading mode and set a turn towards the field. Flight Path Angle (FPA) was active and I leveled the aircraft by setting a flight path angle of zero and leveled at 8000 ft. We were outside of the final approach segment and had previously briefed that if we lost GPS navigation we would discontinue the RNP by turning to the field and either go around or request a visual approach if we were outside of the FAF and stabilized with the field in sight. I asked the FO to let ATC know we were off the RNAV and request a visual approach. The FO requested a vector for a visual approach and ATC gave us a heading and cleared us for a visual approach. I asked the FO to resequence the FMS with a straight in approach which we used to back up the visual to Runway XXL.We debriefed the approach after we shut down but had not realized that we were below a minimum vectoring altitude as we had leveled off above our next expected fix while turning towards the field. As pilot flying I should have maintained my concentration on the aircraft state as opposed to being distracted by the traffic. I was overconfident in my ability to maintain my scan while searching for traffic. Automation management was also a factor as I did not expect the FMS to sequence to green needles with the RNP active. Even in VMC conditions with terrain and the field insight it would have been most prudent to execute the full discontinue procedure and begin a climb to the missed approach altitude.