Riggs National Corp., which owns Washington's biggest bank, reported yesterday that its fourth-quarter profits rose nearly 21 percent to $6.55 million ($1.09 a share) from $5.42 million (90 cents) in the final three months of 1983.

Riggs has shown steady improvement in profits and loan quality in the last three years, after a dismal 1981 in which profits sagged and problem loans, particularly real estate and Latin American credits, soared.

Joe L. Allbritton, who bought controlling interest in the old-line Washington bank in early 1982, has replaced most of the bank's senior management, increased Riggs' already sizeable share of Washington's retail banking market and worked off a large chunk of the bank's problem loans.

For 1984 as a whole, Riggs reported record profits of $26.9 million ($4.49), 15 percent more than the $23.37 ($3.53) reported in 1983. Riggs traditionally has been less profitable than the far smaller American Security Bank, the city's second-biggest institution.

But American Security stumbled badly this year as its once pristine loan portfolio became riddled with problem energy and maritime credits. Following an examination by the Comptroller of the Currency, American Security announced it would take a special $37 million writeoff in the fourth quarter. The bank company will report a loss for the fourth quarter and sharply lower profits for the year.

Riggs, whose assets now total $5.1 billion, reported that its problem assets were $25.1 million on Dec. 31, down from $26.8 million a year ago and far smaller than the $64.3 million in problem assets it had at the end of 1981.

The bank company added $6.7 million to its reserves for loan losses, down sharply from the $22.8 million addition it made in 1983. In 1984, Riggs charged off $5.9 million of loans as uncollectable, while in 1983 its writeoffs were $14.8 million. Riggs' loan loss reserve, at $31.6 million, exceeds its problem assets by nearly $9 million.

Riggs earnings had been reduced in 1983 and much of 1984 because of a successful push to garner consumer money market deposit accounts at a time when loan demand was weak. It invested many of those variable-rate deposits in long-term Treasury securities with fixed interest rates. When rates on the money market accounts rose sharply to levels closer to the Treasury rates, the bank's profit margins were squeezed.

The bank said yesterday that during the fourth quarter, as interest rates declined, it sold many long-term securities and bought short-term securities with the proceeds. The bank said that now its has a far better match of short-term deposits and assets.

Citizens Bancorp -- the Riverdale, Md., bank company -- reported 1984 earnings of $19.2 million ($9.74), 8 percent higher than the $17.8 million ($9.03) it earned in 1983. Citizens, which acquired Peoples Security Bank last March, said that its assets grew from about $900 million to $1.1 billion during 1984.

Citizens has 93 branches in Maryland. Its deposits were $925.8 million at the end of 1984.