Nath's friends and local theatre artistes, who once shared stage with Kher, mourned his demise. Nath, a Kashmiri Pandit by origin, died in Mumbai after a brief illness Friday.
"Nath will always be remembered for the excitement he had whenever Anupam's new movie was about to release," Shimla-based artiste Sanjay Sood told.
Another theater personality Parveen Chandala said Nath had not been well for more than a month.
"He was a familiar face in Shimla. He was often seen strolling on the Mall and chatting with his friends in the coffee house. Normally, he made it a point to visit the coffee house daily, except during winters when he used to move to Mumbai," Chandala, who worked with Kher, said.
"Now, we will miss him in the coffee house."
Sood said during the start of Kher's career in Hindi films, Nath, a former employee with the state forest department, used to carry posters with him.
In Kher's early releases like 'Saransh', 'Karma' and 'Arjun' in the early 1980s, Nath used to carry film posters and loved to show them to his son's friends and fans.
He said during the shooting of "Main Aisa Hi Hoon" in Shimla in October 2004, Nath used to visit the shooting locations regularly.
"For hours, he used to give pep talk to the local artistes during the shooting by narrating about the hard work and love of his son towards theatre," Sood, who also performed in "3 Idiots" and "Kareeb", added.
Kher's class fellow Anil Kumar Sharma said Kher's father was always gladdened with his son's achievements.
"We will miss him on the streets of Shimla," he said.
Kher and his younger brother Raju, also an actor, were brought up and educated in Shimla.
Kher was in this town in July last year along with his parents in connection with an award ceremony of the state police.
"I still remember that it was July 27, 1974 when I left this beautiful city to join the National School of Drama to purse theatre," he said at the function address.
Nath worked with Himachal Pradesh's forest department. He turned 84 Jan 28.
"As I landed in Goa, my brother Raju called from Mumbai to inform me the best dad in the world (our father) is no more," Kher tweeted Friday.