Verma's comment on Twitter was appreciated by Khan who thanked him for his concern.
"Sorry for the trouble at LAX @iamsrk. We are working to ensure it doesn't happen again. Your work inspires millions, including in the US," Verma tweeted.
Khan, who was in the US to visit Yale University, was detained at Los Angeles airport and given immigration clearance only after about two hours.
It is the third time in seven years that Khan has been stopped by US immigration officials at the country's airports.
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The actor expressed disappointment on social media after the incident.
"I fully understand & respect security with the way the world is, but to be detained at US immigration every damn time really really sucks," (sic) the actor tweeted.
Assistant Secretary of State for South and Central Asia in the US Department of State Nisha Desai Biswal also apologised to Khan for the "hassle".
In April 2012, Khan was detained at the White Plains airport near New York for overtwo hours by immigration officials. In 2009, he was detained at the Newark Airport in New Jersey for nearly two hours.