"This falls exclusively into the government's area of competence and it is their decision," she told reporters.
The ECHR ruled on May 31 that Lithuania hosted a secret CIA prison for terror suspects between 2005 and 2006, ordering the country to pay 130,000 euros in damages to Abu Zubaydah, a Saudi Arabia-born Palestinian, over his alleged unlawful imprisonment in Lithuania.
Grybauskaitė then said that Lithuania should not question the court's ruling and would have to comply.
"The ECHR issued its ruling; it is not favorable for Lithuania. The reputational damage has already been done", the president said in late May.
"We are committed to the European Convention on Human Rights and, therefore, we will have to comply with the judgment," she added.
In a reversal of the Justice Ministry's announcement last week that Lithuania would not turn to the ECHR's Grand Chamber, Prime Minister Saulius Skvernelis unexpectedly said on Wednesday that the government would ask for the judgement to be reviewed.
August 31 is the deadline for the government to file an appeal.
The Lithuanian government's representatives told the Strasbourg court that the suspected building in Antaviliai, near Vilnius, was to house an intelligence support center and that the suspected planes had transported communication equipment rather than people to Lithuania.