ANNAPOLIS -- A fierce debate over the role of parents in their teenagers' abortions has opened a rift within the abortion-rights movement as the Maryland General Assembly prepares to confront the volatile issue again.

Although solid majorities in the Senate and House of Delegates agree on a plan to ensure abortion access for adults, their unified front has crumbled in negotiations over whether parents of pregnant minors should be notified in advance.

This discord, coupled with a still-determined antiabortion bloc in the legislature, throws into question the confident predictions that last year's elections guaranteed rapid action on an abortion-rights measure in 1991.

"The antis can win a public relations victory . . . by splitting the pros," lamented Del. Peter Franchot (D-Montgomery), an abortion-rights advocate.

Senate leaders, saying they represent majority thinking in Maryland, insist that parents be notified. But House abortion-rights leaders say they consider a notification provision "anti-choice," contending that it would frighten pregnant teenagers into obtaining dangerous, illegal abortions.

Sen. John A. Pica Jr. (D-Baltimore), a main sponsor of the leadership's abortion bill in the Senate, said parental notice is a must. "They have a choice: Either they accept this or they don't get a bill," he said. "If Roe v. Wade is reversed, the alternative is far worse that what we're proposing."

But Karen Ringen, a lobbyist for Planned Parenthood of Metropolitan Washington, said advocates are not happy with concessions. "Some people think teenagers are a good giveaway . . . . Our view is that nobody is a good giveaway." About one-third of Maryland's abortions are performed on girls under age 18.

A year ago, abortion-rights advocates here were thwarted by a filibuster and confusing, conflicting amendments. Even antiabortion lawmakers and other leaders concede that the legislature appears more willing this year to approve a bill that would maintain the right to an abortion in Maryland if the Supreme Court ultimately overturns Roe, the 1973 decision that recognized a constitutional right to abortion. Unless Maryland law is changed, reversal of the landmark ruling would revive the state's 1968 restrictions that would virtually ban abortions.

Yet beneath the general agreement lies deep division over parental involvement in abortion decisions by minors. Across the country, laws requiring parental notice or consent have grown in popularity since the Supreme Court held last June that such laws are constitutional if they give teenagers some way to bypass parents through the courts or physicians.

Although some abortion-rights lawmakers see the disagreement over parental notification as ominous, others say it reflects a narrowing of differences on the main question of abortion rights.

"It just shows where the debate in this state has moved," said Del. Samuel I. Rosenberg (D-Baltimore), an abortion-rights supporter.

Abortion-rights advocates think several factors are working in their favor this year.

Gov. William Donald Schaefer, who sat out the 1990 debate, declared during his reelection campaign that he personally opposes abortion but would veto any bill restricting a pregnant woman in making her own decision. He has left open the possibility of supporting parental notification.

Senate President Thomas V. Mike Miller Jr. (D-Prince George's) was a late arriving and reluctant leader of the abortion-rights crowd in the Senate last year. Trying to avoid last year's quagmire, Miller personally lined up support this year and mapped out the campaign for passage of an abortion-rights bill.

The abortion-rights leaders in the two chambers agree that the main component of the bill should be unrestricted access to abortions up to the point at which the fetus is able to survive outside the womb. Later in pregnancy, abortions would be allowed to protect the life or health of the woman or if the fetus has serious deformities.

But as Thursday's joint public hearing on abortion approaches, Senate abortion-rights leaders and their counterparts in the House are not in perfect sync. Miller's proposal would also require that the parents of minors be notified before an abortion unless the physician decides the girl is mature enough to give informed consent, that notification could lead to abuse or otherwise would not be in the minor's best interest.

Miller and others argue that a majority of Marylanders want parents involved. And if a new law is to withstand an expected statewide referendum in 1992, it must contain the notification provision, they said.

Others, including Del. Rosenberg, disagree. They contend that any notice provision, even one giving doctors wide discretion, would drive teenagers to seek dangerous, illegal abortions. Moreover, they point to last November's referendum in Oregon, where the issue of parental notice was presented directly to voters for the first time and was defeated decisively.

The Senate leadership's plan on parental notification still would give Maryland one of the most liberal such laws in the nation. Thirty-eight states require parental consent or notice, although those laws are enforced in only 16. Massachusetts, for example, requires that both parents or a judge consent to an abortion. Virginia and the District do not require notice or consent.

As an alternative to notification, Rosenberg and Del. Lawrence A. LaMotte (D-Baltimore-Carroll) have proposed mandatory counseling for girls under 16 seeking abortions that would include a discussion of involving parents in the decision.

But Franchot said, "We should not be seeking mushy concession. The vast majority of Maryland residents want Roe v. Wade -- that's the compromise."

While abortion-rights advocates bicker among themselves, the opponents also are preparing to snipe at all proposals, offer restrictive amendments and, possibly, filibuster again.

Sen. John A. Cade (R-Anne Arundel), a leader of the antiabortion legislators, said he hopes that some restrictions will prevail.

"There's some division on the other side over parental participation," Cade noted. "I assume it will get resolved, but I don't care. That's their problem. We've got enough of our own."