As producer of the film, Kumar made a telephone apology after Peters criticised the acting abilities of Abhishek's wife Aishwarya Rai Bachchan.
"Akshay said 'Sorry' to Abhishek," a source told Mumbai Mirror.
"He respects Aishwarya and the Bachchan family a lot. He is naturally very embarrassed about Russell's remarks."
The Canadian comic-turned-actor reportedly upset industry figures during a recent promotional trip to Mumbai after making derogatory statements about Indian cinema.
"It was a very kind gesture on Akshay's part. Abhishek told him to take it easy. After the call, Akshay felt a lot lighter," added the source.
Indo-Canadian hockey-themed project Speedy Singhs released alongside Shahid Kapoor vehicle Mausam last Friday.