The cemetery, where more than 200 Soviet soldiers killed during fighting against the Nazis in 1945 are buried, was sold due to an administrative error after being incorrectly included in neighboring land deeds.
"Within 30 days the necessary documents will be prepared, and the land will be returned to the local authorities," Laslo Ovary said.
Budapest had earlier assured Moscow that it would stick to the intergovernmental agreement regarding the security of military cemeteries.
Earlier on Wednesday a senior Russian military official, Major General Alexander Kirilin told Hungarian officials that "the cemetery had been maintained in absolutely excellent condition and a new road would be built."
A Russian embassy spokesman, Irina Zvonova said the restoration work at the cemetery has been completed.
In May 2007, the removal of a monument to Soviet soldiers in another ex-Soviet country Estonia led to clashes between protestors and local police, leaving one dead, over 150 injured and more than 1,000 arrested.
The human rights group Amnesty International condemned the situation in Estonia and called on its leadership to respect the rights of ethnic Russians.
Soviet forces liberated Hungary from German forces, which occupied the country, in 1945, the year that WWII in Europe officially ended.
