Captain reported miscommunications with push crew resulted in a ramp conflict during push back.

Narrative

We were operating flight ZZZ to ZZZ1. Parked at gate; doors closed; we asked for a push back clearance. Ramp Control asked us to call Ground for push back to spot XY. We made the call to Ground and they said to give way to airplane behind us and then cleared to push to spot XY. I relayed the exact information to the Ramp Agent. After a short wait we started pushing back; and then the Ramp Agent stopped the push back process and advised that there is an airplane behind us. We queried Ramp Control; while they were busy handling the conflict and talking to the other airplane. After a few seconds; a different Ramp Agent talked to us from the push back tug and informed us that he will have to tow the airplane back into the gate to allow for the inbound airplane to park at gate X. And so we did; and I informed the passengers about the situation. After the airplane parked at gate X; we received a clearance to push back. The rest of the flight was uneventful. The entire situation happened with our airplane nose pointing towards the terminal and so; it was difficult to understand what was going on behind the airplane and how close we were to that inbound aircraft during the push back process. We didn't hear Ramp Control clearing that inbound airplane to gate X. One way to minimize future similar threat is perhaps; for Ramp Control to communicate with Ground to coordinate push back clearances when necessary.