The prosecutors say that Justice Minister Tudor Chiuariu and former Telecommunications Minister Zsolt Nagy abused their positions "against the public interest" when they sold real estate owned by the national post office in April to a private company.
Chiuariu called the request "foolish revenge" and accused prosecutors of abusing their positions. He said they had asked for the investigation of him a day after he asked for two leading prosecutors to be dismissed.
Nagy also denied the charges.
There was no word from Basescu on whether he would approve the investigation. Probes into public officials and former ministers must be approved by the president.
Allegations surfaced last week that Chiuariu and Nagy had sold two plots of real estate to a private company reported to be linked to the ruling Liberal Party.
The Liberal prime minister, Calin Popescu Tariceanu, has not commented on the case.
Romania joined the European Union on Jan. 1 and has been told to clean up high-level corruption.