The Spain international clashed with the Portguese during the Blaugrana's 4-3 Clasico win at the Bernabeu last month, but was quick to deny any wrongdoing.
Pepe responded by calling the 25-year-old a "liar" and Casillas has backed his teammate, slamming his Spain colleague's conduct.
"The image speaks for itself. Pepe has the full backing of the whole side," he said at a promotional event.
"I'm not going to go into more detail. It was a heated moment. Busquets, from my point of view, behaved poorly. When I see Busquets I'll give him a slap."
Casillas has only played for Madrid in the Copa del Rey and the Champions League this season, with coach Carlo Ancelotti preferring Diego Lopez in La Liga, but the 32-year-old is tired of the debate.
"It is a subject that has got tiresome. Those who the boss thinks that should be playing, play. That's that. You have to carry on as you are," he said. "Diego Lopez deserves support and has started a competition and should finish it. I train and compete. It's good for me and the side.
"Diego Lopez is good enough for the national side: of course. Vicente has already shown he believes this. Now Vicente del Bosque must decide. Since Victor [Valdes] got injured he will have been closely following other keepers and will make the best decision."
Casillas also admitted that his side cannot afford to lose to Real Sociedad in San Sebastian this weekend but denied that Cristiano Ronaldo's absence means Ancelotti is prioritizing other competitions.
"We cannot slip up. It is very important and we have to take the three points and then wait. Hopefully there'll be good results for us. With anything other than a win, it would make the league very difficult for us.
"I don't think the league is taking a backseat. The decision was made because [Ronaldo] can't play. Over the last five years he has been superb and always with the side. If he has to stop it's because he needs it.
"He must recover well and be there in the next games. Whoever replaces him will do their best."