The Federal National Mortgage Association said yesterday it will offer 7 million new shares of common stock for sale at a price of $15.875.

The offering, to be made through a syndicate of underwriters headed by Dillon Read & Co., will bring to 72.8 million the number of shares Fannie Mae has outstanding.

Company Chairman David O. Maxwell said proceeds from the sale would go to "support Fannie Mae's efforts to meet the needs of the American people for home mortgage funds."

Fannie Mae is a congressionally chartered, privately owned company that buys mortgages from lenders, thus providing them with funds to make further loans. It is the largest entrant in this secondary mortgage market and currently owns roughly one out of every 14 home mortgages in the country.

But the company, which traditionally has relied primarily on debt to finance its mortgage holdings, has been battered by the volatile interest rates of the 1980s. High interest rates on its borrowings have outpaced yields on older, low-interest mortgages in its portfolio, and the company has lost money in three of the past four years.

Fannie Mae has adopted various tactics to deal with interest-rate risk, including packaging many of its more-recently-purchased loans into mortgage-backed securities, which are sold to investors.

Maxwell said Fannie Mae has been seeking to build up its equity and felt current conditions favored a stock offering.

The company noted that the underwriters have an option to buy an additional 700,000 shares at the offering price if the initial offering is oversubscribed.

Fannie Mae's stock, traded on the New York Stock Exchange, has ranged between 10 7/8 and 19 3/8 during the past year. It closed yesterday at 15 3/4, down 1/8.