Did a US general threaten to open fire on British troops - in WWII?!

The General in question being Mark Clark, commanding the Fifth Army in Italy and the British troops the Eighth Army, slogging up the other side of the Apennines.

I’ve seen it claimed a few books an alarming quote attributed to Clark aimed at Alexander, insinuating that if the Eighth Army tried to take Rome before his Fifth Army, he’d order his men to open fire on them!

What the hell was going on? Did he really threaten the troops of his ally if they advanced on Rome before him? Sounds more like rival Fronts of the Red Army, why didn’t Eisenhower or - since he was busy with D-Day - Marshall or even Roosevelt relieve him immediately of command?

Same general Clark carried out the order to murder civilians in the Abbey of Monte Cassino.
General Sir Harold Alexander had given orders and Clark did object, but when ordered to he followed them.