Air carrier Captain reported a critical ground conflict during taxi with an aircraft under tow. The Tower Controller cleared the Captain to cross a taxiway and confirmed the towed aircraft would give way; which it failed to do.

Narrative

We landed uneventfully at ZZZ and began the long complicated taxi process to our gate. A ground controller gave us instructions to continue taxiing and hold short of another taxiway much further down range. They made no mention of aircraft along our intended pathway. We were then switched over to tower who would coordinate our crossing of a runway.While taxiing; a 737 was under tow and approaching our intersection from the left. I was unsure if they would stop given their current speed; so I asked the FO to confirm with tower that this aircraft was going to give way to us. Tower answered us in a condescending and confident manner that aircraft would give way to us and for us to continue taxiing our aircraft. Several seconds later; I brought our aircraft to a sudden stop. The 737 under tow did not stop; and had I followed towers confident assertion; it is very likely a ground contact event would have occurred.Upon stopping the aircraft; we spoke with tower who now had a very different tone in their voice. We advised them we were remaining stopped until they clarified taxi coordination on their end. They claimed the 737 was supposed to stop but their ground movement was occurring on another frequency. They sounded humbled and asked if we wanted that frequency to ask any questions. We professionally declined and advised them we were now ready to safely continue our taxi.