Wikileaks' Editor-in-Chief, Kristinn Hrafnsson, said in a statement that there was "no doubt" that Ecuador had "tampered" with the belongings it had sent to the US.
Manning has offered multiple reasons for refusing to testify, but fundamentally says she considers the whole grand jury process to be unacceptable.
Assange, 47, was removed from the embassy last month after seven years as the Ecuadorian government withdrew his asylum protection, and was arrested for breach of bail conditions.
Swedish prosecutors said at the time they felt they were unable to take the case forward while Assange was inside the Ecuadorean embassy.
The support group, Sparrow Project, said in Thursday's statement that Manning was released after 62 days.
British police arrested him last month after Ecuador revoked his political asylum.
Assange appeared in court within hours of his arrest, and a judge found him guilty of breaching his bail conditions.
Assange, 47, was kicked out of the Ecuadoran Embassy last Thursday after his political asylum was revoked, putting an end to his almost seven-year stint.
Two far-left German MPs, Heike Hansel and Sevim Dagdelen of Die Linke, and a Spanish Green member of the European Parliament, Ana Miranda wanted to prevent Assange's extardition to US.
Assange's father, John Shipton, on Sunday urged Australia to bring his son home.
'DFAT (Department of Foreign Affairs) and the prime minister should in a nuanced way do something,' Shipton told Melbourne's Sunday Herald Sun.
Trump extolled WikiLeaks more than 100 times, and a poster of Assange hung backstage at the Republican's debate war room, during the final weeks of the 2016 presidential campaign.
WikiLeaks' publication of Democratic emails stolen by Russian intelligence officers during the 2016 election season hurt Clinton's presidential campaign.
In 2006 Julian Assange built an online platform that offered an anonymous, encrypted path to leak computerized files without fear of exposure.
I asked Great Britain the guarantee that Mr Assange will not be extradited to any country in which he could suffer torture or face the death penalty, President Lenin Moreno said.