Sixty British parliamentarians joined campaigners on Wednesday in urging Formula One to commission an independent inquiry into the human rights impact of the Bahrain Grand Prix.
Rights groups said in an open letter to chief executive Stefano Domenicali that they also wanted him to seek "redress for those victims of abuses directly linked to your activities in Bahrain."
Signatories included Human Rights Watch and the Bahrain Institute for Rights and Democracy (BIRD).
The Gulf kingdom is hosting the season-opening race, Bahrain's biggest and most-watched sporting event of the year, on Sunday.
Bahrain's 2011 race was called off due to civil unrest and the grand prix regularly draws criticism from rights campaigners who accuse the government of using the positive publicity to 'sportswash' the situation.
Seven times Formula One champion Lewis Hamilton said last December, after Bahrain hosted two races, that he had been moved by a letter from the son of a man facing the death penalty.
The Briton assured activists he would not let human rights issues go unnoticed.
A Formula One spokesman said it and the governing FIA believed the sport could be "a force for good" in bringing different cultures together.
"We have always been clear with all race promoters and Governments with which we deal worldwide that we take violence, abuse of human rights and repression very seriously," he added.
"Our human rights policy is very clear and states that the Formula One companies are committed to respecting internationally recognised human rights in its operations globally.
"Where possible we monitor and audit activities in host countries that relate directly to the staging of an event and behind the scenes we have meaningful discussions with all hosts about our values and the standards that we expect."
A Bahrain government spokesperson told the Guardian newspaper the kingdom had "put in place internationally recognised human rights safeguards."