The Federal National Mortgage Association, a $32 billion corporate giant, is fighting to prevent the government from excerting stronger control over its operations in the mortgage market.

Usually called Fannie Mae, the profit-making company, which was spun off by the government in 1968, is resisting legislation that would add public members to its board of directors and require it to disclose information like publice agencies under the Freedom of Information Act.

The Carter administration is sharply divided on the issue. Some high officials of the Department of Housing and Urban Development favor more public control to induce Fannie Mae to invest more heavily in low-income housing. The Treasury Department is opposed.

Fannie Mae has hired the Washington law firm of Williams & Connolly to furnish legal ammunition against the move by Sens. William Proxmire (D-Wis.) and Alan Cranston (D-Calif.). In a memorandam, the firm has declared that the legislation "is designed to undermine shareholder control" of Fannie Mae policies and would dilute stockholders' property rights.

Proxmire contended yesterday that the company's board "is overwhelmingly on the side of private interests and has little consideration for the public interest. There is no consideration for the needs of low-income housing. Even the so-called public members on the board represent the industry."

At stake is influence over one of Washington's most peculiar instiution, one that has changed from an obscure public agency in 1968 to a wealthy corporation that pays its president, Oakley Hunter, 130,000 a year, and has amassed a profits record any purely private corporation would envy.

It recorded record profits in 1976 of $127 million and boasts a portfolio of mortgages amounting to more than $32 billion. Its dividend payments rose form 33 cents a share in 1972 to 88 cents in 1976 and last February the directors voted another increase - the seventh in seven years.

It was chartered in 1968 as a private, profit-making corporation to buy up mortgages from banks and other lenders and thus promote liquidity in the mortgage market. But although privately owned, it has a number of ties to the government that have the effect of giving it power to borrow money cheaply and increas its profits.

Its debentures and short-term notes are classified as "agency securities," which means they can be purchased by banks and savings and loan companies insured by the federal government.

Most important, if Fannie Mae gets in trouble, it has a $2.25 billion line of credit to rely on at the Treasury. And HUD has a general regulatory power over Fannie Mae.

Under its congressional charter, the President appoints five of the 15 directors (three of the five must be from the real estate and banking industries). The other 10 are elected by stockholders. The Proxmire-Cranston bill would add four new members to be chosen by the President from the public. The result would be a 19-member board with nine votes supposed to represent the public.

Fannie Mae's crities concede it has accomplished its basic purpose of injecting funds into the mortgage market in hard times. In the housing slump of 1973-74, Fannie Mae pumped about $7 billion in for mortgages when money was extremely tight.

The main question is whether Fannie Mae, which benefits from its ties to government, has carried out the other public-purpose aspects of its charter. Congress instructed the HUD Secretary to see to it that the corporation assign a reasonable portion of its mortgage purchases to the national goal of housing for low and moderate-income families.

Proxmire and other crities argue that in its pursuit of profits. Fannie Mae has sought out the low-risk mortgages on suburban housing and steered relatively clear of inner-city neighborhoods, Lenders who want to sell their mortgages to Fannie Mae follwo that lead, it is argued, and don't lend money in older city neighborhoods.

"Fannie Mae imposes criteria on underwriters that tend to discourage mortgages in urban neighborhoods," said HUD official Darel Grotehaus. "They insist on the homogeneity of neighborhoods and on relatively new neighborhoods. And that's bad for urban areas."

James E. Murray, a senior vice president, concedes that "we're not down in the bombed-out areas of lots of those cities, but no one else is either."

He denies that current Fannie Mae mortgage-buying standards deliberately filter the low-income sections of cities out of the mortgage market. Early in its life, however, "we were very careful (on buying mortgages) and so lots of the lenders were reluctant to get into the risky neighborhoods," he said.

But now, he adds, 30 per cent of the corporation's $32 billion portfolio is invested in low-and morderate-income housing within central cities. "Our average loan is for $17,000, so they can't be such very expensive properties," he said.