A "terrible atmosphere of fear and lies" has enveloped Rhode Island because of its month-old banking crisis, says a thrift threatening to prosecute rumormongers it blames for a run on it.

In a newspaper ad Tuesday, Old Stone Bank asked readers to give it the names of people it accused of spreading rumors about its financial condition. Depositors began a run on the thrift Thursday, withdrawing at least $10 million, Old Stone President Theodore Barnes said.Noting that state law prohibits spreading lies about a bank's financial status, the thrift said it would give the names to state prosecutors.

"We need to fight these rumors head-on with the truth, and we must put an end to the terrible atmosphere of fear and lies that caused them to flourish," read the ad in The Providence Journal-Bulletin.

Rumors have abounded since Gov. Bruce G. Sundlun ordered 45 banks and credit unions closed Jan. 1 after their private insurer collapsed. Most have reopened, but about $1.3 billion in deposits remains frozen. Sundlun announced plans Tuesday for repaying depositors whose money is tied up.

Old Stone, with $3.7 billion in assets, is insured by the federal government and was not among the institutions closed.

But thrift officials said a Cable News Network report on the state's troubled financial institutions included a picture of Old Stone.

"People have been very nervous about the credit union situation and when they saw Old Stone, they panicked," said Patricia E. Pyne, spokeswoman for the thrift. "And Rhode Island being such a small state, they told their friends and neighbors, and they panicked."

Barnes said customers withdrew at least $10 million from certificates of deposit. He declined to say how much was taken out of other accounts, but American Banker, a trade newspaper, estimated the total run at $20 million.

Ms. Pyne said some money was coming back this week as the thrift let people redeposit without penalty.

CNN spokesman Steve Haworth said CNN Headline News ran a story on Old Stone on Saturday that it clarified later that day.

Old Stone was cited in a New York Times story earlier in the month as one of the country's most troubled thrifts, a report its executives strongly contested. The bank said in its year-end earnings report released earlier this month that it earned a profit of $2.9 million in 1990.