My son is 4.5 years and has been the same for at least 18 months if not longer, he was diagnosed as moderate asd at 3 years old. He's a big lad aswell so even worse as he's capable of really hurting another child, makes me sweat taking him out.
I can say though after a rough year of all sorts of behaviour specifically the attacking other kids for no reason at all, drove me insane with it, but we have been out with my friend and her 2 year old today and my son hasn't pushed, swiped, smacked, pinched, scratched, nothing! Just cuddled.
He is still supervised very closely to avoid any mishaps and I am 'that' parent who helicopters at all times to avoid it happening, but it's how it has to be, but the outbursts towards the other kids have reduced down gradually and this past few weeks I haven't seen it happen at all, nursery said they had seen a reduction in the behaviour also, I'm pleased to say.
Stressful times while your in the midst of it though.
All I can suggest is keep on supervising being ready to intervene, telling him to use 'kind hands' or a favourite of mine is in a stern voice say no we don't push (smack, bite, insert whichever behaviour) we cuddle instead. Bit strange getting your child to cuddle a random child he'd picked on, but he started to get the idea.. and now often immediately goes to hug a child.
I just apologise to the parent as I'm sure you already do, some are more understanding than others though. Not much more you can do other than hope for it to stop.