The officials were arrested last month for backing exiled opposition leader Rasul Guliiyev in a conspiracy to topple Aliyev, who succeeded his father as president.
"I wanted to give support to Guliyev and gave money for that too," Akif Muradverdiyev, a former presidential aide to Aliyev, said in the broadcast late on Tuesday.
The arrested officials, looking nervous, were shown sitting around a table, wearing suits.
A total of 12 people have been arrested in the case, the National Security Ministry and law enforcement agencies said, making it the biggest political crackdown in the Caspian Sea state for years.
Ali Insanov, the long-serving health minister, Fikret Yusifov, a former finance minister, and Fikret Sadykhov, a member of parliament who headed the state-owned chemical firm Azerkhimya, and Muradverdiyev were among those shown. "I fell into a trap and made a political mistake," Sadykhov said.
Insanov said he had committed unconstitutional acts and had written a letter of penance to the president.