* CEO was owner of failed tiny lender Szechenyi Bank
* Decision on resignation offer to be made in coming days (Adds detail)
BUDAPEST, Dec 8 (Reuters) - The head of Hungary's debt agency AKK, Istvan Torocskei, has tendered his resignation, Economy Ministry State Secretary Gabor Orban said on Monday.
Orban said in a video posted on the government's website that Torocskei had been majority owner in the tiny Szechenyi Bank, which was shut down by the central bank on Friday amid concerns about its capital reserves and violation of rules of prudent operation.
"Istvan Torocskei has tendered his resignation to the ministry, and the resolution of this issue, a decision will be made in the coming days," Orban said.
The government holds a 49 percent stake in the lender.
The Economy Ministry and the AKK could not immediately comment on emailed questions. Torocskei's deputies at the AKK are Laszlo Borbely and Laszlo Buzas.
Under Torocskei, the AKK shifted focus on domestic sources of funding as part of government efforts to cut reliance on foreign investors, who hold about 40 percent of Hungary's debt, exposing the country to shifts in global sentiment.
Last month the central bank said it had opened an investigation into Szechenyi Bank and imposed restrictions on customer withdrawals.
On Friday the central bank said in a statement the operation of Szechenyi Bank had become "unsustainable" and any further operations would have posed a threat to the interests of customers, and to meeting its obligations.
The Economy Ministry's Orban said Torocskei's efforts to recapitalise Szechenyi Bank earlier this year fell through partly because of the Russia-Ukraine conflict and because the government could not increase capital in the lender due to legal obstacles.
Szechenyi had a share of 0.14 percent of the banking sector based on assets, the central bank has said, adding it posed no risk to the stability of the Hungarian banking sector. (Reporting by Gergely Szakacs; Editing by Andrew Roche)