Officials of the Legal Services Corp. have awarded large grants to three conservative groups whose political objectives closely mirror those of the Reagan administration.

The three grants, totaling more than $1 million and awarded without competitive bidding, were approved by Legal Services Corp. President Donald P. Bogard on Sept. 30, the last day of the fiscal year. Congress had ordered the corporation to spend its $275 million budget before the year ended.

The administration repeatedly has tried -- without success -- to persuade Congress to eliminate the corporation, which provides free legal assistance to the poor.

James Streeter, a spokesman for the Legal Services Corp., did not respond to telephone requests for information about the grants.

The corporation also has not responded to requests for copies of the grants from Reps. Barney Frank (D-Mass.) and Bruce A. Morrison (D-Conn.), members of the House Judiciary Committee with a special interest in the corporation.

Congressional sources said yesterday that Judiciary Committee Chairman Peter W. Rodino Jr. (D-N.J.) was expected to ask the General Accounting Office to investigate whether the three groups are eligible for funds under the Legal Services Act.

Copies of the three contracts, obtained by The Washington Post, show that one for $337,000 went to the Constitutional Law Center in Cumberland, Va. The center, which was incorporated July 5, is headed by James McClellan, a conservative constitutional scholar and former aide to conservative Sen. John P. East (R-N.C.).

Bogard, in a Sept. 30 letter to McClellan approving the one-year grant, said the center would "provide direct delivery, technical assistance, training and publications on legal issues concerning the protection of the constitutional rights of the poor."

McClellan has written extensively opposing expansion of criminal defendants' rights, abortion rights and the ban on school prayer.

On the Cumberland center's seven-member board of trustees are several law professors, including Robert D'Agostino of the Delaware Law School. He is a former Justice Department official.

D'Agostino was a candidate for president of the Legal Services Corp. in 1982, but his name was withdrawn because of negative publicity involving two incidents.

One was a memorandum he wrote at Justice in 1981 suggesting that blacks are "more disruptive in the classroom on the average" and would benefit from programs for the emotionally disturbed.

The other was a report that he hit a Delaware Law School secretary in the head after a 1978 argument and paid her medical expenses in return for her not pressing criminal charges. D'Agostino contended that he acted in self-defense after the woman attacked him "fingernails first."

McClellan said by telephone that he is committed to "protecting the constitutional rights of the poor. The traditional Legal Services mold . . . has been to disregard the rights of individuals . . . in order to use the corporation to achieve political goals. We intend to protect individuals, not misuse our authority to accomplish political ends . . . . I reject the idea that only the left wing knows how to protect the poor."

A grant of $400,000 was made to the Oakland Urban Legal Foundation for developing programs to increase private lawyers' participation in the representation of poor people. The administration has promoted the idea of replacing the Legal Services Corp. with private lawyers to provide no-cost or reduced-cost services for the poor.

The third grant, for $337,000, was awarded to the National Center for the Medically Handicapped, in Indianapolis, headed by James Bopp Jr., an attorney who has been prominent in the fight over handicapped infants' rights.

This center, which was incorporated Sept. 5, plans to provide technical assistance, training and publications on "legal issues concerning treatment of the critically or terminally ill handicapped and medically dependent poor persons," according to Bogard's letter to Bopp.

Rep. Frank said in an interview that he believed that the Indianapolis grant might help poor people, but he described the other two as "simply ideological."

"These groups are pretty far out," he said, adding he hoped the Judiciary Committee would hold hearings on the grants when Congress reconvenes in January.

One legal services observer, who asked not to be identified, challenged the Indianapolis grant because the makeup of its board of directors may violate the Legal Services Act. Elected officials of state and local governments generally are excluded, he said, because those governments are often targets of the Legal Services Corp.

According to the center's incorporation papers, the seven-member board includes a state representative, a state senator and the head of a county welfare department who has been a frequent target of legal-services suits.