Opponents of abortion bitterly attacked the Supreme Court yesterday, accusing it of legalizing "abortion on demand" in its latest ruling and vowing to push through Congress a constitutional amendment to ban the practice.

Sen. Roger W. Jepsen (R-Iowa) predicted that the 6-to-3 ruling will backfire and help him and other abortion critics pass anti-abortion legislation. Jepsen and Rep. Henry J. Hyde (R-Ill.) are co-authors of the "respect human life" bill to ban federal abortion funding and extend legal rights to the unborn. President Reagan has endorsed the bill.

"There's absolutely no question about that backlash ," Jepsen said. "The furor and emotion that this has generated will help us. The Supreme Court is completely out of their jurisdiction. Maybe it will be the straw that broke the camel's back."

Sen. Bob Packwood (R-Ore.), a leading Senate defender of the right to abortion, said he was "delighted" by the court's decision. "The court said . . . that this is a constitutional right that state legislatures cannot nibble away at . . . . If 'right-to-life' forces want to upset it, they have to do it with a constitutional amendment . . . ."

At issue in yesterday's ruling were appeals from Missouri, Virginia, and Akron, Ohio. The cases had raised hopes among abortion opponents that the court would reverse its landmark 1973 decision in Roe v. Wade legalizing abortions in certain circumstances.

Instead, a majority of the justices affirmed that a woman's right to privacy includes her decision on abortion and overturned local laws that tried to limit that right.

Supporters of the right to abortion were ecstatic at the decision, despite the fact that Sandra Day O'Connor, the first woman to serve on the court, wrote the dissent.

Janet Benshoof, director of the American Civil Liberties Union's reproductive rights project, which brought the Akron case, called the decision "a total victory for a woman's right to chose abortion."

But the enthusiasm for the decision was overshadowed by fear of a new push for a constitutional amendment banning abortion.

Nannette Falkenberg, executive director of the 150,000-member National Abortion Rights Action League, said, "The decision will simply convince anti-choice groups to intensify their efforts to restrict abortions . . . . We will see new strategies to prevent abortions and increased harassment of women seeking them."

Judy Lichtman, executive director of the Women's Legal Defense Fund, said abortion-rights groups are prepared to fight those efforts. "We've fought them. We've won, and we'll fight them again," she said.

Abortion opponents made it clear that they, too, are ready to fight for a ban on abortion and for legislation to take the issue out of the jurisdiction of the federal courts.

Sen. Orrin G. Hatch (R-Utah) called the Supreme Court decision an "abomination." Hatch has proposed an amendment saying that the Constitution does not guarantee women the right to abortions. Hatch said his proposal will reach the Senate floor before July 4, but he conceded that it has little chance of passage.

Gary Curran, speaking for the 120,000-member American Life Lobby, said, "We are very disappointed with the Supreme Court decision. It is clear that a majority of the justices . . . care little or nothing for the humanity of the unborn . . . . This is proof positive that via judge-made law, we have abortion on demand in America.

"The Supreme Court thinks they are a super legislature for every city, town, county and state in America. This will spur us to enact a constitutional amendment to ban abortion . . . and other human-life bills which would remove the question of abortion from the federal courts entirely."

Richard A. Viguerie of Conservative Digest said the ruling "displays an incredible insensitivity to the health needs of women. This ruling will delight those abortionists who are only interested in running as many women as possible through their clinics so as to maximize their profits. The court has, in effect, put its stamp of approval on assembly-line abortion clinics.

"In every abortion, at least one person dies, but there is no need to risk the life of the mother as well . . . . She deserves some protection from the people who might take advantage of her while she is distraught."

Douglas Johnson of the National Right to Life Committee said the ruling "demonstrates the extremism of the court on abortion . . . . It underscores the need for congressional action . . . and for the appointment of judges who will not impose their pro-abortion extremism on the nation. The court has defended the interests not of women but of the assembly-line abortion industry . . . . The issue is now drawn very starkly."