American Security Corp., the District's second-biggest bank company, reported profits of $6.2 million (53 cents a share) in the second quarter, as the bank continued a slow recovery from a disastrous 1984.

Its 1985 second-quarter earnings were 36 percent higher than the $4.6 million (40 cents) it reported in the second quarter of 1984, when growing loan losses began to eat into the bank company's profits.

Earnings remained depressed in the third quarter last year, and American Security reported a fourth-quarter loss of $11.9 million. The loss was attributed to a $37 million provision for loan losses that American Security took after an examination by the comptroller of the currency, the agency that regulates federally chartered banks.

The second-quarter profit was the biggest the bank has reported since the $7.2 million earnings recorded in the first three months of 1984, before loan losses began to escalate.

American Security said yesterday that the improved performance over the second quarter of 1984 reflects "a $5.9 million decrease in the company's loan-loss provision, a $2.4 million increase in net interest revenues and a reduction in the rate of operating expense growth."

American Security, with assets of $3.9 billion, set aside $4.6 million to cover potential loan losses in the three months ended June 30 compared with $10.5 million in the second quarter of 1984. Provisions for loan losses are subtracted directly from earnings and added to a special reserve. When a bad loan is written off, it is subtracted from that special reserve.

American Security's loan-loss reserve totaled $52.7 million at the end of June compared with $27.5 million a year ago.

The bank said its problem assets totaled $144 million on June 30 compared with $101.6 million on June 30, 1984, and $142.4 million at the end of last year. The problem assets included $134.7 million in troubled loans and $9.3 million of real estate on which the bank has foreclosed .

About half of the bank's troubled loans are concentrated in three areas: real estate, energy and marine. The bank has $18.7 million in problem international loans.