The District of Columbia is moving for the first time to regulate the sale of money orders by private firms - a business relied upon by thousands of low-income residents who do not have checking accounts used by most people to pay their bills.

The gap in city law that leaves the industry without supervision was dramatized in 1973 by the collapse of a Nevada-based firm that had many sales outlets here. Last year, another firm, with money orders that were sold through several credit unions, also collapsed. The credit unions made up the loss, although they were not required to do so.

A hearing was held last week by the city council's consumer affairs committee on proposed legislation that would regulate money order firms. Although the proposal drew the general support of three Washington money order companies, several witnesses suggested changes in the details of the proposal. The measure, sponsored by council member John A. Wilson (D-Ward 2), the committee chairman, would license and provide for government supervision of all the companies, set financial standards for their operation and require that the companies and their sales agents be bonded to protect consumers against possible losses.

The U.S. Postal Service is the nation's largest seller of money orders, but the business has declined sharply in recent decades as more Americans began maintaining their own checking accounts. Some banks also sell money orders. In most central city areas, the biggest sellers of money orders are specialized independent firms, which arrange with liquor stores, groceries and other retailers to act as agents. The companies and the agents split the fee paid for each money order, typically around 50 cents.

Henry Zetlin, vice president of the Federal Express Service Corp. of Glen Burnie, Md., one of the largest independent firms operating in Washington, estimated that as many as one-third of all District families use money orders. Zetlin asked Wilson to add language to the bill that would require sales agents to keep the money paid for money orders in funds separate from the storekeeper's own receipts.

Wilson refused. "The agent works for you," he told Zetlin. "He is your agent."

Barry Mersky, a vice president of Global Money Order Co., a Washington-based firm with about 50 agents in the city, urged Wilson to drop a requirement that each sales agent be bonded for $5,000 to protect against theft or default.

Some agents do such a small volume of business, he said, that the cost of the bond would be prohibitive. He cited one agency, the management of a nursing home, that sells money orders as an occasional but vital service for its elderly and infirm patients.

The third supporter of the legislation was Wilbert Rozansky, partner with his wife in the FW Money Order Co.

The measure would put supervision of money orders under a city agency, which has not been chosen. Banks, telegraph companies and other money order firms already supervised by other government agencies would be exempt.