After Nobel laureate Grass announced he was in the German SS as a teenager for a short period at the end of World War II, Walesa sent an ultimatum to the Baltic Polish city of Gdansk, Belgrade's B92 radio-television said Friday.
Walesa led shipyard unions in revolt against the communist regime in 1980.
The former president demanded Grass give up a honorary citizenship he received in 1993 from Gdansk for assistance to Polish dissidents and his contribution to a reconciliation between Germans and Poles.
Grass was born in Gdansk in 1927 when it was called Danzig and is of German and Polish ancestry.
Walesa welcomed Grass' admission of his Nazi past, but said he believed it was a publicity ploy to improve the sale of the German author's just-published biography.
Walesa said, "If it proves to be a publicity trick, and the Gdansk authorities (aren't) doing anything, I will have no other (choice) but to renounce my own honorary citizenship," Belgrade's Beta news agency reported.