From July this year, SZTFH will limit deposits and withdrawals from bank accounts that engage in illegal gambling on unlicensed websites.
In turn, Hungarian banks will refuse card payments that are made to unlicensed sites, also from July onwards.
SZTFH said that any winnings gained while gambling on illegal sites may not be paid to customers after the restrictions come into place.
In April, SZTFH fined a private, unnamed individual HUF30m (£70,000/$87,000/€79,000) for organising a real estate lottery. Lotteries with prizes such as real estate cannot be legally organised by businesses or private individuals.
In March SZTFH implemented technical measures in response to amendments in its Gambling Act. Under the amendments, customers can now have balances with multiple operators, and players can now cash out early if the game they are participating in allows it.