Sri Lanka's largest political party on Saturday asked Facebook to protect the identity of its supporters, fearing a crackdown by what it called the "illegal" government.
The Indian Ocean nation has been in crisis since last month with two men claiming to be prime minister, MPs brawling in parliament and the administration paralysed.
In chaotic scenes in parliament this week, Rajapakse lost two votes of no confidence but he is refusing to go and Sirisena has yet to acknowledge the motions.
On Saturday Wickremesinghe's United National Party (UNP) wrote to Facebook chief Mark Zuckerberg asking the US firm not to cooperate with Rajapakse's administration.
"We urge Facebook to refrain from disclosing information about... users of the platform to any officials of the illegal government unless it is properly sanctioned by a court of law," the UNP said.
The UNP had also complained that its official page was blocked by Facebook on Thursday ahead of a mass rally it organised to express solidarity with Wickremesinghe, who insists he is still prime minister.
Sirisena ordered a ban on Facebook across Sri Lanka in March after blaming it for spreading hate speech and fuelling inter-communal violence that led to the deaths of three people and destruction of property.
Since then, Facebook had said it was deploying more staff to identify and remove inflammatory material from Sri Lankan users.
This week Sri Lankans had to rely on social media to watch their lawmakers fighting and throwing chilli powder after the main telecommunications company stopped its live broadcast.