Prosecutors had said the group's central structure violates its designation as a "foreign agent" by not marking all its publications with the label as required by law but Memorial's lawyers and founders deny any serious violations.
Russia's Supreme Court has ordered the closure of Memorial, the country's most prominent rights group, which chronicled Stalin-era purges and symbolised the post-Soviet democratisation.
Judge Alla Nazarova ordered on Tuesday the closure of Memorial International, the organisation's central structure, over breaches of its designation as a "foreign agent" by not marking all its publications with the label as required by law.
The "foreign agent" legislation, which carries Stalin-era connotations, brands organisations receiving foreign funds as acting against Russia's interests.
During the hearing, a prosecutor said Memorial "creates a false image of the USSR as a terrorist state and denigrates the memory of World War II".
The Interfax news agency quoted a lawyer for Memorial – which has said the lawsuit was politically motivated – as saying that it would appeal, both in Russia and at the European Court of Human Rights
Memorial's lawyers and founders have denied any serious violations, saying its material was properly marked and that only an insignificant number of documents may have been missing the tag.
Other cases against rights group
The case was heard by the Supreme Court because Memorial International is registered as an international body.
The organisation, founded in 1989 by Soviet dissidents including Nobel Peace Prize laureate Andrei Sakharov, believes it will become a victim of the repression it was founded to keep at bay by the end of the week.
The latest hearing in the trials comes after Russia blocked the website of the OVD-Info rights monitor, which works with Memorial, on the weekend saying it promoted terrorism and extremism.
OVD-Info has tracked opposition protests and provided legal support to victims of political persecution, while Memorial has compiled a list of political prisoners that includes Putin's main domestic opponent Alexey Navalny.
Navalny was jailed in February on old fraud charges and has since seen his organisations banned as "extremist" and all of his top allies flee the country.
Prosecutors had also demanded a court close Memorial's Human Rights Centre, accusing it of condoning "terrorism and extremism" in addition to breaches of the "foreign agent" legislation.
A Moscow court will hold a new hearing in that case on Wednesday.
On Monday, a court in the northwestern city of Petrozavodsk increased a prison sentence for the head of Memorial in Karelia, Yury Dmitriyev, to a total of 15 years.
His supporters say he is being punished for his work locating and exhuming mass graves of people killed under Soviet dictator Joseph Stalin's rule.
Sentenced last year to 13 years in prison on what his supporters say were fabricated child sex charges, the 65-year-old will now spend two additional years in prison.
Memorial is a loose structure of locally registered organisations, with Memorial International maintaining the network's extensive archives in Moscow and coordinating its work.
The group has spent years cataloguing atrocities committed in the Soviet Union, especially in the notorious network of prison camps, the Gulag.
Memorial has also campaigned for the rights of political prisoners, migrants and other marginalised groups, and highlighted abuses especially in the turbulent North Caucasus region that includes Chechnya.
Supporters say its closure would signal the end of an era in Russia's post-Soviet democratisation process, which began 30 years ago this month.