By Steve Olafson

OKLAHOMA CITY (Reuters) - A Tulsa family who lost their house in a sheriff's sale after their bank assured them their mortgage would be modified on Monday received $20,000 from an Oklahoma settlement with major banks for deceptive mortgage practices in the U.S. housing bust.

Oklahoma, which carved out its own settlement with major banks to compensate victims of unfair foreclosure practices, began handing out checks on Monday that could be 10 times or more what a national settlement offers the fraud victims.

The state expects Oklahoma victims of deceptive mortgage practices to receive $5,000 to $20,000 under its $18.6 million agreement with Bank of America, Citigroup, JP Morgan Chase, GMAC and Wells Fargo.

Payments under the national settlement with the five banks could be about $2,000 to borrowers who were not properly offered loss mitigation or lost their homes to foreclosure.

Some victims outside Oklahoma could see payments as low as $840 after all the claims are processed, said Diane Clay, spokeswoman for Oklahoma Attorney General Scott Pruitt.

"This is a vindication of the risk he took," Clay said. "He took a lot of criticism for it."

Pruitt presented Zach and Melissa Zuniga of Tulsa with a $20,000 check and more checks are expected to be issued each week through the end of January.

The Zuniga family, like many others, were victims of "dual tracking," a process in which they were assured their mortgage would be modified while foreclosure measures were under way, the attorney general's office said.

The family had just 14 days to move out of the house that had been in the family 23 years and then received a third modification package proposal from Citigroup three days after their home was sold, the attorney general's office said.

"These families endured horrendous conduct, lost their homes in many cases and deserve more than an 'I'm sorry' and a few hundred dollars," Pruitt said in a statement.

About 700 people in Oklahoma have applied for relief from the state's compensation fund, compared with states such as California and Nevada where tens of thousands of owners lost their homes due to unfair foreclosure practices.

(Reporting by Steve Olafson; Editing by Eric Walsh)