Three civil liberties groups yesterday opened a drive for laws to overrule Supreme Court decisions that they think have been shutting the doors of the federal courts to minorities, the poor, prisoners, advocates of unpopular causes and victims of government misconduct.

Heartened by the advent of the Carter administration, they met yesterday to form the nucleus of a coalition intended to persuade Congress to offset a court that, they charged, "has turned its back on its fundamental responsibility."

The federal courts often provide the only forum in which the powerless can gain legal protection for rights and liberties, the groups said in a statement. But a majority of the nine justices has been not merely rejecting their claims, but has been refusing "to consider them at all," the statement charged.

The groups are the American Civil Liberties Union, which has 275,000 members, and two small organizations, the Committee for Public Justice and the Society of American Law Teachers.

They sponsored an all-day national conference on access to justice that was marked by unusually harsh denuciations of the principal architects of the portested decisions, Chief Justice Warren E. Burger and Justice William H. Rehnquist.

Ralph J. Temple, legal director of the ACLU's National Capital Area branch, characterized the justices - both appointees of President Nixon - as "powerful political personalities" with an ideology that would make them "perfectly at home" in the repressive regimes of the Soviet Union, Chile or India.

ACLU general counsel Frank Askin, a Rutgers University law professor, accused "the Burger-Rehnquist court" of an "essential lawlessness" revealed in part by manipulation of "legal concepts and analyses to . . . reach preconceived results."

Several speakers emphasized a mitigating factor: the federal judicial system is overloaded with cases, as Burger repeatedly has pointed out.

And Sen. Gaylord Nelson (D-Wis.), who addressed a luncheon meeting of the approximately 200 participants, characterized the response of Congress to "the caseload crisis" as "insensitive, inadequate and occasionally hypocritical."

But "the rights of the innocent will be lost as surely as the rights of the guilty" if "lawless decisions" of the Supreme Court are allowed to shortchange constitutional rights "in the name of law and order or judicial efficiency," Nelson said.

Agreeing, the sponsors of the conference said in their statement that the caseload of the federal courts must be lightened "by curtailing jurisdiction in areas which do not involve constitutional rights."

Nelson and Sen. Charles Mc. Mathias Jr. (R-Md.), who opened the conference, held in the Russell Senate Office Building, are sponsors of bills favored by the groups.

ACLU Chairman Norman Dorsen, who presided at the conference, said that in seeking remedial legislation he hopes to have the cooperation of Attorney General Griffin B. Bell. Bell made a surprise appearance Friday night at a reception held by the conference's sponsors.

Dorsen said that he and Bell have had a private talk about such legislation and will meet again - at the Justice Department - within two weeks.

The major goal of the three groups is to enlarge the right to sue. "Some of the Supreme Court's procedural roadblocks define who can bring an action so narrowly that, for practical purposes, no one can bring it," their statement said.

"Other decisions permit certain claims to be brought but make bringing them so burdensome or make the available remedies so narrow that a victory is too expensive to pursue at all," it continued.

In addition to asking Congress "to remove the jurisdictional roadblocks" from the legal path of those "who most need" the protection of the federal courts, the statement called on President Carter to appoint judges "who will view preserving the Bill of Rights as their primary responsibility."

As examples of denials of the right to sue, speakers cited decisions that barred low-income and minority persons from challenging the constitutionality of a zoning ordinance excluding them from suburbs and from challenging an Internal Revenue Service ruling making it easier for "charitable," tax-exempt hospitals to cut back services to them.

In two other cases, said University of Kentucky law Prof. Robert Allen Sedler, the court barred suits alleging constitutional violations by the government on the ground that the plaintiffs - citizens and taxpayers - had not suffered "injury in fact."

Prof. Burt Neuborne of New York University Law School said that federal trial judges with lifetime appointments generally provide far more effective protection of constitutional rights from state and local encroachment than do state trial judges, who often are subject to political pressures.

Slaveholders, he recalled, had access to the federal courts when they sought judicial enforcement of their constitutional rights to the return of fugitives. The descendants of slaves, he said, also should be able to seek redress in the federal courts, rather than being confined by Supreme Court decisions to state courts.