"A new chapter will begin soon," Orban told the daily Napi Gazdasag in an interview published on Friday. "We are in non-stop talks with banks and I hope we can sign an agreement soon. We want burdens on banks to be bearable, and in exchange the sector should play a much bigger role in financing the economy."

Orban's government has levied one of the European Union's highest bank taxes on the sector and forced banks to repay to clients about 3 billion euros (£2.3 billion) after courts deemed past lending practices unfair.

The country is likely to record more than 3 percent economic growth in 2014 after years of stop-and-go recession but analysts expect the expansion to slow next year as European Union funds are utilised at a slower rate.

Orban declined to say whether the new deal would entail a cut in the bank tax.

"It is too early to talk specifics," he said. "Everybody is interested in a long-term, stable solution. And the chances to get one are good."

The government, which has advocated a majority Hungarian ownership in the bank sector, achieved that goal through buying MKB Bank from Germany's BayernLB and Budapest Bank from General Electric.

However, Orban said he wanted to see the banks in Hungarian hands but with the exception of a few specialised banks that have been in state ownership for a long time, private owners were more desirable.

Asked who in Hungary has the capital to buy banks now, he said:

"There are strong Hungarian banks, and there is also the stock exchange. There are several techniques. What I do not support is the method Hungary once followed, selling everything to foreigners outright."

He did not rule out that the government itself would buy more banks if sensible opportunities arose.

Central Bank Governor Gyorgy Matolcsy, a close ally of Orban, has said for the past year that as many as four foreign banks could exit the country. The largest commercial banks have all said they would remain.

Hungary's top banks include home-grown OTP (>> OTP Bank Nyrt), Austria's Erste (>> Erste Group Bank AG) and Raiffeisen (>> Raiffeisen Bank International AG), Italy's Intesa SanPaolo (>> Intesa Sanpaolo SpA) and UniCredit (>> UniCredit SpA), and Belgium's KBC (>> KBC GROEP).

(Reporting by Marton Dunai; Editing by Toby Chopra)