The fund started buying back its shares in the second week of May, and it has bought back a 1.5% stake so far, paying RON112.67 million.
The fund initially had a total RON120.3 million earmarked for buybacks, to rein in share price declines. The operations are brokered by Wood&Company Financial Services.
Fondul Proprietatea was set up in 2005 to compensate Romanians whose properties were seized during the communist era.
The fund was floated on the Bucharest Stock Exchange on January 25.
Proprietatea shares rose 0.22% early Tuesday, to RON0.4609. (EUR1=RON4.2402)