The government has until now categorically denied that the country hosted such a detention facility for terror suspects.
Mustafa al-Hawsawi, 51, is currently being held at the US military detention facility in Guantanamo Bay. The man, whom the US suspect of involvement in the September 11, 2001 terror attacks, was captured in Pakistan in 2003.
The man's defense lawyers say in their petition that he could have been brought to Lithuania in February or October 2005 and taken out of the country in March 2006.
Deputy Justice Minister Irma Gudziunaite confirmed to BNS that the Strasbourg-based court's office had granted Lithuania's request to extend the deadline for filing its position regarding the claim until October 31.
According to information available to BNS, the deadline was earlier set for August.
"The extension of the deadline was requested because this is a complex, large-scale case; the related pre-trial investigation by the Prosecutor General's Office is still ongoing. (The request) was also due to the need to coordinate the position with the relevant state institutions," Gudziunaite told BNS.
This is the second claim brought against Lithuania in the Strasbourg court in relation to allegations that the country hosted a secret CIA prison more than a decade ago.
Last May, the ECHR ruled that the CIA had secretly held Abu Zubaydah, another Saudi terror suspect, in Lithuania.
The court ordered Lithuania to pay Zubaydah 130,000 euros in damages for human rights violations. The government has placed the money into a depository account.
In the first case, Lithuanian government officials told the Strasbourg court that the suspected building in Antaviliai, in the outskirts of Vilnius, had been "an intelligence support center" and that the suspected planes had transported communication equipment rather than people to Lithuania.
A pre-trial investigation into the allegations that Lithuania hosted a secret CIA detention site has been ongoing in the country, but no formal suspicions have been brought yet.