A Government source told PA news agency on Saturday that Mr Stewart has informed Chief Whip Simon Hart that he wishes to surrender the party whip until a possible appeal of his conviction is resolved.
Rishi Sunak faced immediate calls to suspend Mr Stewart as a Tory MP following the conviction, for which he was handed a £600 fine. The 74-year-old had been attending an event hosted by the Bahraini embassy when protester Mr Alwadaei shouted "Bob Stewart, for how much did you sell yourself to the Bahraini regime?"
During a heated exchange, Stewart replied: "Go away, I hate you. You make a lot of fuss. Go back to Bahrain."
Chief magistrate Paul Goldspring found the MP guilty of a racially aggravated public order offence and gave him the £600 fine, with additional legal costs bringing the total to £1,435.
Mr Goldspring, despite mentioning Stewart's "immense positive character", remarked: "I accept he is not racist per se, but that is not the case against him.
"Good men can do bad things."
Stewart, asked for his thoughts on the allegations of racial hostility, had earlier said: "That's absurd, it's totally unfair, my life has been, I don't want to say destroyed, but I am deeply hurt at having to appear in a court like this."
The MP declared: "I am not a racist."
He continued: "He was saying that I was corrupt and that I had taken money.My honour was at stake in front of a large number of ambassadors. It upset me and I thought it was extremely offensive."
Labour and the Liberal Democrats led calls for Prime Minister Rishi Sunak to act against the "totally unacceptable" behaviour of the 74-year-old Conservative backbencher.