My car was parked. A car rear ended my car and pushed it into another parked car. Thing is, the person who caused the accident won't take blame for my car hitting the other car. Does his insurance have to pay for both or will my insurance have to pay for damages to the car hit by mine?

If your car was parked and hit while parked, any damages resulting from him hitting you are his responsibility.

Tell the owner of the other car to file a claim with the insurer of the car that hit you. But you NEED to report this to your insurer as well.

Ye, I told my insurance exactly what happened. Thing is the other car was left because of bad weather conditions and no one on the road knew who owned it. I left my details on windscreen along with the persons responsible.
The other parked car got in touch with me finally and has said that he has called the other party and they are not willing to accept responsibility.
But I have told my insurance what happened and there are witnesses.
Guess I'm worrying about nothing but thank you for answering.

Call the other party back and tell them don't listen to the other driver. You have the other driver's insurance info. Give it to them and tell them to file a claim with the other driver's carrier. It doesn't matter what the other driver says about accepting responsibility. Now if their insurance carrier refuses to accept responsibility that's a different matter.

In that case, the third party needs to contact their carrier who will then sue the carrier for the responsible party.