And five years after receiving insider data on the Swiss bank holdings of over 2,000 Greeks -- the so-called Lagarde list -- only 136 cases have been conclusively checked, he added.
The left-wing government of Prime Minister Alexis Tsipras has accused its conservative and socialist predecessors of protecting business friends from tax checks.
The list had been sent in 2010 to then socialist finance minister George Papaconstantinou by Christine Lagarde, International Monetary Fund chief and at the time French finance minister. Lagarde had got it from an HSBC whistleblower.
A few years later, it emerged that three members of Papaconstantinou's family had been on the list, but their names were excised and they escaped scrutiny.
Papaconstantinou denied any wrongdoing but a court in March found him guilty of tampering with the data.
Alexiadis on Friday said that the statute of limitations on the Lagarde list investigation was due to expire on December 31, but the government would take steps to extend the prosecution period by another year.
He added that the government was also poring through bank transfers and data on Greeks with property in London and yachts registered in the Netherlands in search of undeclared income.
"We are not going to cover up anything," Alexiadis said.