Marc Anwar, 45, joined "Coronation Street", the world's longest-running TV soap opera, in 2014 as a member of the show's first Muslim family.
But he was sacked from the show after the Sunday Mirror newspaper published screenshots from his private Twitter account, which hit out at India over the Kashmir dispute.
"Indians killing our Kashmir brothers and sisters," he wrote.
"I would like to offer my sincerest apologies to anyone that I may have offended with my tweets on Friday evening, and especially people from India," he said in a video he uploaded to YouTube on Monday.
"This was never my intention. The language was unacceptable. I feel I've let a lot of people down: my family, my friends and my former colleagues."
"Coronation Street", which began in 1960, became the longest-running soap opera in the world in 2010.
Set in a fictional suburb of Manchester in northwest England, it remains one of Britain's most-watched programmes with around eight million viewers.
Guest stars have included Prince Charles, the heir to the British throne.
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