Riggs National Bank has received preliminary approval from the Comptroller of the Currency to open two new branches, after agreeing to make mortgage loans to nondepositors and to take other steps to increase lending to low- and moderate-income people.

Riggs plans to open new branches at 1201 Pennsylvania Ave. NW and 600 Pennsylvania Ave. SE.

The District's largest bank came under fire last year from citizens' groups as a "rich man's bank." The D.C. Bank Campaign and the Metropolitan Washington Planning & Housing Association accused Riggs of red-lining, or refusing to make mortgage loans in poor areas.

The groups said that between 1972 and 1975, some 72 percent of all Riggs single-family residential mortgages loans, or 79 percent of the bank's single-family mortgage money, went to areas of the city west of Rock Creek Park. Under the Community Reinvestment Act, red-lining constitutes grounds for rejecting an institution's application to open branch offices.

The charges triggered a broad review of mortgage-lending practices in the Washington area by the Comptroller of the Currency. Officials said at the time they felt there was a need for more comprehensive information of the kind they obtained in connection with their regular bank examinations.

The Office of the Comptroller did not find that Riggs had red-lined, but it did outline some "areas of improvement" in an April 23 letter to Riggs President Daniel J. Callahan III. This week Callahan wrote back to list what improvements Riggs has made.

He stated: "We have discontinued our past policy of accepting mortgage applications only from existing depositors and will, in the future, entertain and review applications from nondepositors." He added, "While we will not reduce our credit standards, we will entertain applications from all who submit them."

Callahan further promised to establish "an on-going dialogue with real estate brokers in low- and moderate-income areas" and to make Riggs' consumer credit services known to the community at monthly meetings of the advisory neighborhood commissions. He added that Riggs would be willing to meet with community groups on a continuing basis, "but we are only willing to talk to recognized, responsible groups and not just complainers."