ROME (Reuters) - Italian Prime Minister Matteo Renzi criticized European Central Bank Governor Mario Draghi for not having done more to resolve Italy's banking woes when he held a key Treasury job in Rome in the 1990s.

Renzi's rare public criticism of Draghi came on the day Italy's third-largest lender, Banca Monte dei Paschi di Siena <BMPS.MI>, said that the ECB had asked it to cut its bad debts by 40 percent within three years, heaping more pressure on Rome to stabilize its banking system.

After taking power in 2014, Renzi's government introduced reforms aimed at strengthening the country's cooperative banks, but several are struggling to stay afloat and a bailout fund took control of Veneto Banca last week after the ECB said it had to raise capital or close.

"If the measures concerning the cooperatives had not been taken by us but by the centre-left government that first put them forward, but was not strong enough to enact them in 1998 ... then we would not have this problem," Renzi said.

The prime minister said that Draghi was director general of the Treasury at that time, with Carlo Azeglio Ciampi serving as economy minister.

"And if people had the strength and intelligence to keep politics out of the banking system a bit before we did it ... we would not have had cases like Monte dei Paschi di Siena," Renzi told a meeting of his centre-left Democratic Party (PD).

Monte dei Paschi has been in crisis mode for years, hit by a disastrous acquisition on the eve of the financial crisis, losses from risky derivatives trades and bad debts accumulated during Italy's worst recession since the Second World War.

(Reporting by Crispian Balmer; Editing by David Goodman)