The Reagan administration, backed by private companies seeking a piece of the secondary mortgage market, urged a Senate subcommittee yesterday to reject a request by the Federal National Mortgage Association for broader loan-buying powers.

Fannie Mae and the Federal Home Loan Mortgage Corp., with the endorsement of home builders, Realtors and other housing trade groups, are seeking permission to purchase larger and more varied loans and, in the case of Fannie Mae, authority to buy commercial as well as residential mortgages.

The two government-sponsored institutions have been seeking these expanded powers for several years, and somewhat similar proposals stirred little controversy in the Senate last year.

But this year, the requests are drawing heavy fire from both the administration and from emerging private rivals who say they fear that further unleashing of the two giant institutions would stifle the new companies' growth.

In addition, reports surfaced this week accusing Fannie Mae of pressuring private companies with which it does business to support the proposals

At yesterday's hearing of the Banking subcommittee on housing, Fannie Mae President David O. Maxwell called the reports "extremely distressing" and said "it is not the policy of Fannie Mae to make business decisions based on legislative positions" of other companies.

"I will stake my personal integrity and I will certainly stake my company's on the fact that we do not engage in that sort of matter, and it is not our policy or practice and it never will be."

Fannie Mae and Freddie Mac are the major players in the secondary mortgage market. Each year they buy billions of dollars' worth of mortgages and put them in their own portfolios or package them and resell them to investors. The purpose of the system is to replenish the cash supplies of savings and loans, mortgage bankers and other lenders so they in turn can make more loans.

Currently, both are forbidden to buy loans larger than $108,300--limits that both Maxwell and Freddie Mac chief Kenneth J. Thygerson said exclude major segments of the home-buying market, particularly in high-cost areas. Freddie Mac is seeking to have the limit raised to $125,000, while Fannie Mae would like to see it done away with and replaced by a formula tied to the association's annual secondary market activity.

In the past, the Reagan administration has favored making both organizations completely private. That is still the administration's goal, the Office of Management and Budget's Lawrence A. Kudlow told the subcommittee yesterday, but right now the White House is anxious to do nothing that might "disrupt the agencies or the promising housing recovery."

In the meantime, Kudlow said, the administration thinks "it would be unwise to make any substantial increase in the scope of Fannie Mae's activities" since the association and Freddie Mac have special advantages because of their relationship to the government. Primarily, these advantages work to lower both organization's operating costs and allow them to raise money more cheaply than a fully private firm could.