The Justice Department yesterday announced it will go to court to block Household Finance Corporation (HFC), the nation's largest consumer loan company, from buying American Investment Co., of St. Louis, on grounds the acquisition would lessen competition in the consumer loan business.

The government's action threatens to frustrate Household's ambitious efforts to expand and invigorate its consumer finance division.

HFC's more than 2,000 branch offices currently command 10 percent of the consumer loan market. The company loaned a total $2.9 billion to 2.5 million borrowers in 1977. But the finance giant has run up against increasingly stiff competition from banks and credit unions which, thanks to more liberal finance laws, have been allowed to make small high-interest consumer loans.

Hoping in a single leap to broaden its customer base, HFC last September announced plans to purchase American Investment, a medium-sized consumer loan business with 450 offices in 29 states. Under the terms of the proposed deal, HFC has offered to pay a total $76 million in cash for outstanding shares of American's common and preferred stock.

American Investment earned $4.8 million on revenues of $145.1 million in 1977 and had assets worth $500 million. HFC earned $138.7 million on revenues of $9.0 billion and had assets totaling $3.9 billion.

"As far as we're concerned," said James Pinkerton, spokesman for HFC, "we intend to pursue the acquisition and defend it vigorously."

Justice officials gave few details about their objection to the acquisition. The department issued a brief three-paragraph statement saying only it would soon file a civil antitrust action in Chicago, site of HFC's headquarters, challenging the proposed acquisition as a violation of the section of the Clayton Act that prohibits mergers or acquisitions that would lessen competition or would "tend to create a monopoly."

In the past two decades, Household has diversified away from its traditional loan business through a wide variety of purchases. Today, HFC subsidiaries manufacture thermoses, sell groceries and rent cars in addition to loan money. Less than half of the corporation's earnings last year came from consumer lending. A favorite tag line around HFC offices is that 8 out of 10 Americans buy from the company, though most probably don't realize it.

More recently, HFC has concentrated on expanding its consumer loan division. The expansion has taken place on several fronts. In addition to the proposed purchase of American Investment, HFC has bought two insurance companies, a California savings and loan association and a string of industrial banks in Colorado. Also, it has launched an income tax service and set up a commercial leasing operation by buying the staff of American Fletcher Leasing Corporation.

Eventually, Household officials hope to integrate these financial services into its network of neighborhood offices and thereby create a national chain of financial supermarkets capable of handling the complete financial needs of a family.