An air carrier Captain reported they were holding short of a taxiway waiting for an aircraft to pass when they observed a different aircraft taxiing across their path that would not have room to clear their aircraft. The reporter instructed the other aircraft to stop on Ground Control frequency.

Narrative

We landed XXL in ZZZ; exited 1; and held short of XXR. After 7-10 minutes or so we were cleared to cross XXR ON 1 and join 2; and monitor Ground. We crossed the runway; and switched over to Ground. We weren't given any other instructions other than to monitor Ground and join Taxiway 2. Aircraft Z was taxiing on Taxiway 2; from right to left. Since I didn't know who had the right of way; and wasn't given instructions from Ground on who should follow who; I slowed down and stopped for the them to pass first; then I would follow behind them. We were trying to get a word in with Ground; but it was a very busy night. We were fully stopped on 1; holding short of Taxiway 3. As we were fully stopped; Aircraft Y; was taxiing on 3. It didn't appear that they were slowing down on 3; as we were clearly in the way; waiting for Aircraft Z to pass.It was very clear to me and the First Officer that they didn't have enough space to pass in front of us. How it wasn't clear to them I'll never know. I turned on my taxi light first to brighten my aircraft up; but they kept coming. I turned on my landing lights; which were very bright; yet they continued. I then immediately turned all my lights on and off repeatedly; while getting an edge wise on the radio and told Aircraft Y to stop. At that point they stopped. They were stopped in front of us; too tight for any aircraft to move out of each other's way. I told Ground what happened and that either us or the Aircraft Y would need to be towed away from each other for spacing purposes. After about 20 to 30 minutes a tug for each aircraft came to create separation. They had to close Runway XXR for a few minutes just to push us back the 10 to 15 ft. or so to create enough space to separate the aircraft. At that point we were towed to the gate. Mainly if it came down to one thing; Aircraft Y either didn't see us (which I don't know how considering I was lit up like a Christmas tree); or they continued taxiing thinking they could taxi in front of us; even though it was way too tight to do so. They should have stopped if they were unsure; as we did waiting on Aircraft Z. We were holding in that position for a solid minute to minute in a half. When in doubt stop. Also it was a very busy night; and it was hard to get a word in with Ground. There was no clarification on whether we needed to wait for Aircraft Z or if they should wait for us. Both of us took to safe approach and slowed down; with us giving way to them. Maybe some clarification from Ground; on whether we needed to follow Aircraft Z or they follow us. The main thing though is Aircraft Y should have stopped if they saw us. It was way too tight for them to go in front of us; or maybe they didn't see us; but I find that highly unlikely.