* City finance director resigns over budget discrepancy

* Previous mayor convicted of fraud last week

* Jefferson County faces multibillion dollar debt (Adds quote, paragraph 3, detail)

By Verna Gates

BIRMINGHAM, Ala., Nov 3 (Reuters) - The finances of Alabama's biggest city, Birmingham, are stable despite the resignation of its finance director in the wake of a corruption scandal, the city's acting mayor said on Tuesday.

Finance chief Steve Sayler resigned late Monday over $20 million discrepancy in the city's budget for the current fiscal year, Acting Mayor Carole Smitherman said.

"Our city is in sound financial condition. Both the citizens of Birmingham and the national rating services can stand assured that Birmingham is sound," said Smitherman.

His departure raised further questions about Birmingham's finances after former mayor Larry Langford was found guilty last week of charges ranging from bribery to fraud.

Smitherman told a city council meeting she had reassured credit ratings agencies after they called to ask about city finances following the Langford verdict.