Do you make a 3 year old say sorry when he clearly doesn't mean it?

Our son pushed a little girl at the park yesterday because she was on 'his' swing. I made him say sorry. He said it to the ground, in a sing-song voice, and went straight back to the swing. Her mother smiled politely. I felt worse than before. My partner thinks a forced sorry teaches nothing and we should just take him away and talk about it later. I grew up having to apologise immediately and clearly, so that is my instinct. What do you do in the moment, at this age?