Tennessee banking authorities yesterday closed United American Bank of Knoxville in what is the fourth biggest bank failure in U.S. history.

The Federal Deposit Insurance Corp. immediately assumed control of the bank, which has about $760 million in assets and $590 million in deposits, and began to search for another bank to buy the failed institution and take over its accounts.

Late last night, the FDIC said the First Tennessee Corp. of Memphis, the state's largest bank holding company, had acquired United American, The Associated Press reported.

Regulators cited "large and unusual loan losses" at United American, the centerpiece of a chain of five banks controlled by Jake Butcher, a politically prominent Tennessean who was the guiding light behind last year's World's Fair in Knoxville.

Although the bank had been a major lender to developers of the World's Fair, some of whose loans are in arrears, the bank's loan problems went far deeper than the fair, federal sources said. One source said bank regulators are looking at loans made to the bank's officers.

"It's a case where money kept going out in loans, some of them substantial, and it stopped coming in. The bank was getting into a liquidity problem and had to borrow from the Federal Reserve and try to dig itself out of a hole. Then the auditors came in and said, 'The hole is too deep to dig out of,' " a source said. Butcher and other bank officials were unavailable for comment yesterday.

The bank reported a loss of $2.3 million last year and had predicted a loss for 1983 as well. But sources said FDIC told the bank its 1982 set-aside for potential loan losses (which is directly deducted from profits) was far too low and that the bank's loss should have been higher.

According to federal sources, FDIC examiners identified at least $50 million in loans that they felt the bank should write off as total losses and another $100 million to $150 million in "questionable" loans. The bank had less than $45 million in capital. A loan write-off of $50 million would throw it into insolvency.

Butcher, the Democratic candidate for Tennessee governor in 1978 and an active political supporter of former president Jimmy Carter, is a major distributor of Amoco products and John Deere equipment. He entered the banking business when he picked up the pieces of the Hamilton Bank in Chattanooga, which failed in 1976.

Butcher apparently spent last week trying to find another bank willing to take over the struggling bank or make a substantial contribution to its capital. The bank also advertised heavily on radio and television, telling depositors the institution was sound, promising to reopen Monday morning and reminding them that all accounts up to $100,000 are insured by the FDIC.

After news leaked out last week that the bank was having difficulties, depositors began a "mini-run" on the bank, sources said.

The FDIC sent auditors into all of Butcher's banks several months ago and reportedly ordered the Knoxville bank to add more capital and to hold down its new loans so stringently that the bank "essentially was out of the lending business," one source said.

Last week United American filed suit against the FDIC to try to lift some of those restrictions, but details of the suit are unavailable because, at the bank's request, a federal judge sealed all court papers.

The end came for United American early yesterday morning when the Federal Reserve system, the lender of last resort for all financial institutions, called in an $80 million loan it made to United American to shore up the bank's liquidity, or cash, position. Sources said the Fed pulled the loan, made through its so-called discount window, after Tennessee Banking Commissioner W.C. Adams reluctantly agreed with the FDIC that the bank was insolvent.

Since the bank was state-chartered, Adams had to make the binding determination that it was insolvent.

By law, the central bank cannot make loans to a bank that is insolvent, although the Federal Reserve could have called the loan anyway.

Anxious FDIC officials gathered yesterday in the 24th floor of the agency's Atlanta headquarters to receive bids for the failed bank's deposits and its solid assets. The agency, acting for the first time under a new bank failure law enacted by Congress in late 1982, courted offers from banks all over the Southeast and as far away as New York City.

The bank's failure ranked behind the 1974 failure of Franklin National of Long Island, ($1.4 billion in deposits), the U.S. National Bank failure in San Diego, in 1973, ($930 million), and that of the Banco Credito y Ahorro Ponceno of Puerto Rico in 1978 ($614 million).

Butcher, the 46-year-old chairman, was eased from authority last week by the bank's directors, although he retained the formal title at the Knoxville bank as well as at the four other bank's in which he is the major shareholder.

He also has an interest in several other banks in Tennessee and Kentucky with his brother C.H. Butcher.