Mr Puri made the comments at Delhi’s Ramlila ground when activist Anna Hazare was on a 12-day hunger strike.
Mr Puri described MPs as “illiterate, rustic and useless”.
MPs have protection from insults and parliament sent Mr Puri a notice asking him to explain his comments.
A spokesman for Mr Puri confirmed to the BBC that the actor wrote a letter to the speaker about a month ago, but refused to divulge the details.
Parliament has the power to summon individuals for a reprimand if they refuse to apologise.
A string of corruption scandals has angered many Indians and Mr Hazare’s campaign had received widespread support and a great deal of media coverage.
Mr Puri had taken the stage and addressed the crowd during Mr Hazare’s fast.
After his comments were criticised by several MPs, he apologised.
“I am unhappy with myself over the terms that I used. I agree I could have used better language, but I was caught in the moment and so used those terms,” he told the IBN7 news channel.
He was awarded an honorary OBE for his contribution to the British film industry in 2004.