The colleagues are the front-runners for the Formula One drivers' title this season and have gone wheel-to-wheel in several races.
Hamilton took advantage of wet weather at the Hungaroring to surge through the field, finishing the race third after starting from the pit-lane.
Having jumped ahead of Rosberg, whose race was wrecked by the safety car being deployed on lap nine, Hamilton was ordered to allow the German to pass him as he had an extra pit stop to take.
However, with Rosberg over a second behind him, Hamilton refused to yield, telling his race engineer: "I'm not slowing down for Nico. Get close and then he can overtake me."
And after the race, Hamilton was stunned he had been ordered to play into his team-mate's hands as both chase top spot in the standings.
"Obviously I am aware that I was in the same race as him, just because he had one more stop than me doesn't mean I am not in same race," Hamilton argued.
"If I let him past then he could pull away and come back at me later.
"I was very, very shocked that the team would ask me to do that.
"He didn't get close enough to overtake, I was not going to lift off and lose ground to Fernando [Alonso] or Daniel [Ricciardo], so it was a bit strange."
Rumours of a conspiracy surrounding alleged support for Rosberg from the Mercedes team have dogged the constructors' championship leaders this week.
Though they have been swiftly brushed off by Mercedes officials, a stoney-faced Rosberg is keen to seek talks into why Hamilton did not follow team orders.
The German told Sky Sports: "I didn't want this [team orders], it was the team that informed me that he was going to let me past, that was it.
"I don't know what happened we need to discuss internally, it's better.
"I'm still ahead on the championship going into the summer break I can sit down and think about everything then come back full attack."