Klepetar has sued the National Gallery and the Czech Culture Ministry, claiming the return of the artifacts, but so far unsuccessfully.
The court also turned down his proposal that the law on easing certain wrongs caused by the Holocaust be changed. The law allows for the return of the works of art seized from the Jews during the war only to the offspring of the original owners, but not to more distant relatives.
Consequently, Klepetar, who is Popper's great-nephew, has no right to the paintings under the law.
The Constitutional Court rejected his complaint as unsubstantiated.
Popper, who lived in Brno, south Moravia, before the war, was one of significant art collectors and patrons. His collection allegedly included valuable paintings by Flemish, German, French and Spanish artists from the 15th to 19th centuries. He died in the ghetto in Lodz, Poland, with his wife and their only daughter during WWII.
Klepetar and his brother have claimed the collection from the Czech state for years. They say at least 43 paintings from the Popper collection are in the National Gallery.
The district and city courts rejected their claims. The Supreme Court returned the case to lower-level courts in 2007, but the claimants lost the dispute again.
Under the law on easing certain wrongs caused by the Holocaust, the Czech state is obliged to return the artifacts seized from the Jews between September 29, 1938 and May 4, 1945 to the original owners or, if they died, to their spouses or children.
The Holocaust victims lost thousands of artifacts during World War Two. Many of them ended up in various galleries and museums.
The legislation enables to return at least part of the stolen heritage to the families of the original owners. The Czech state, for instance, dealt with the return of the collections of lawyer Emil Freund and art patron Arthur Feldmann.