F1 chiefs say they will "continue to investigate" alleged human rights abuses in Bahrain.
Representatives met with campaigners on Wednesday to discuss Najah Yusuf, who was jailed two years ago.
Protest groups including Human Rights Watch and the Bahrain Institute for Rights & Democracy claim Yusuf had been given a three-year sentence because she protested against the 2017 race.
Bahrain authorities say Yusuf's jailing was not related to the grand prix.
The sport has been accused by human rights groups of sending "an appalling message" over the matter.
Liberal Democrat peer Lord Scriven met F1 officials on behalf of the campaign groups. He outlined claims of alleged sexual assault during Yusuf's interrogation as well as claims that a coerced confession was used to convict her.
Following the meeting F1 bosses said the sport is "committed to respecting internationally-recognised human rights in our operations globally and we take all such responsibilities seriously".
A statement continued: "As part of that commitment, we obtain from every national promoter of a Formula 1 Grand Prix its commitment to respect internationally recognised human rights.
"We continue to remind all promotors, including Bahrain, that peaceful protest at all our events is a democratic right."
Lord Scriven said he had been told F1's general counsel Sacha Woodward-Hill would look into the matter.
"I am relieved that Sacha and Formula 1 have expressed genuine concern and have an open mind to investigate further the particular circumstances which have led to Najah's imprisonment and the violations of her human rights since her arrest," Lord Scriven added.
The parties have agreed to hold another meeting once further investigations had been carried out.
Staged for the first time in 2004, the Bahrain Grand Prix has been one of the most controversial races on the F1 calendar.
It was cancelled in 2011 after pro-democracy protests were crushed. At least 35 people were killed; protesters claimed the death toll was far higher.
In 2013 a group of British MPs called on then-F1 boss Bernie Ecclestone to cancel the race again amid further unrest in Bahrain. However, recent races there have passed off without incident.