Bollywood superstar Shah Rukh Khan said Tuesday he will cut back on visits to the United States, especially with his family, after he was questioned by immigration officials at a New York-area airport. Khan told reporters Tuesday after returning to Mumbai that the incident had been “blown out of proportion.” But he said the questioning - which included requests for the names of people who could vouch for him - embarrassed him. He said he will travel to the US less frequently. “Of course I will visit the US if I have to go for my work. But I will go less often. If I have three things to do, I will club them together and go just once,” he said. “And certainly, I wouldn't like to travel with my family to the US.” Khan, 44, appealed to fans to stop protesting. Meanwhile, in a new twist to the controversy, California Governor and Hollywood superstar Arnold Schwarzenegger's office has invited him to dinner at Washington DC. Khan is aware of the invitation but he is yet to decide whether he wants to go back to the US so quickly. The dinner stands postponed to Sept. 20. It is not known whether he will accept it or not.