He also requested the Indian government to take the matter up with Pakistan.
Anupam was to attend the Karachi Literature Festival which begins on Friday. However, while 17 out of the 18 Indians who were due to go received their visas, the 60-year-old says he was "singled out".
"Have been informed that Pakistan MoFA has denied permission for my visa to participate in the Karachi Literature festival. Sad to have been denied visa on second time in a year, while around 17 people will participate in the Karachi Literature Festival as guests," Anupam posted on Twitter.
At a press conference he called in Mumbai, Anupam said: "I was excited to go there.. there is a lot of possibility of lot of things that can happen so I changed my shooting schedule accordingly.
"For the last 15 days my papers were ready for the visa... my point is I am not angry with anybody.. I am hurt, upset and I am somewhere feeling wanting to know the reason out of 18 people why only I have been singled out," he said, adding that he was a "mature person" and it was "important to deal with situation with lot of grace".
"I am capable of fighting my own battles, I am capable of dealing with my own life. I will request the government of India to take this up and yet continue the process of peace with Pakistan. I appreciated my prime minister going there and starting the peace process," he said, referring to Modi's sudden visit to Lahore on his way back from Kabul.
Meanwhile, Manzoor Ali Memon, a diplomat at the Pakistan High Commission, told IANS: "He (Anupam Kher) has not submitted (any) visa application. Please check out from him if he has any receipt."
At this, Anupam said when he heard Pakistani diplomats say that he had not applied at all, "I thought the truth need to come out".
"I am not here to expose anybody. I am just here to share my disappointment. I can be an true Indian and without criticizing Pakistan, I can go there. I would like to go there and would like to talk about my country," he said at the press conference.
Upset about the visa denial, Anupam had tweeted: "Has my visa been denied because I speak about India's rich tradition of tolerance or I am a Kashmiri Pandit who may expose Pak terror nexus? Indian government welcomes Pakistan based writers, artists, actors etc. Pakistan government bans entry of Indian actors. Why fear a free dialogue.
"Didn't Pakistan Ministry of Foreign Affairs red flag my name to Pakistan High Commission in New Delhi? Why hide facts deliberately? Pakistan High Commission should know their own rules. #KarachiLitFest had given my name to authorities one month back and have my name in every poster."
His son, actor Sikandar Kher, said that his father's uninhibited views on numerous social and political issues could have ruffled feathers and could be the reason why the veteran actor was denied a visa.
It was in May last year that the actor was denied a visa to Pakistan. He was to visit Lahore for an event hosted by an NGO, but according to reports, back then it was denied on security grounds.
This time, he was invited as a guest at the three-day Karachi Literature Festival. Among the Indians who will be present at the literature festival are Laxmi Narayan Tripathi, Rahul Singh, Om Arora, Urvashi Butalia and Ashok Chopra.