The Bush administration called on the Supreme Court yesterday to uphold new restrictions on abortion, backing a New Hampshire parental- notification law that has no exceptions for pregnant girls whose health is at risk.

The administration's filing adds a new element to this summer's Supreme Court confirmation proceedings of John G. Roberts Jr., because he could be the pivotal vote in the case, which is to be argued late this year and decided next year. If confirmed, Roberts will replace Justice Sandra Day O'Connor, who was co-writer of the 1992 decision requiring that states not impose an "undue burden" on exercising the right to abortion.

In filing a friend-of-the-court brief in the case, the administration weighed in for the first time in an abortion rights case before the Supreme Court. In his filing, Solicitor General Paul D. Clement argued that "there is no need for a general health exception to a parental-notification statute."

The 2003 New Hampshire law would require parents to be notified 48 hours before a girl's abortion, unless the procedure were needed to prevent her death. Judges could bypass the notification requirement if they thought the girl was sufficiently mature or if abortion without notification was in her best interest.

Thirty-three states have parental-notification laws. The court has not yet clarified whether O'Connor's "undue burden" standard means such laws must have an explicit exception for cases involving a girl's health. The Supreme Court defined an "undue burden" only as a law that imposes a "substantial obstacle" to abortion seekers "in a large fraction of cases."

The U.S. Court of Appeals for the 1st Circuit in Boston struck down the New Hampshire law as unconstitutional last year, citing the 1992 ruling. In appealing the case, Ayotte v. Planned Parenthood, New Hampshire argued that the proper legal standard was not the 1992 case but a 1987 Supreme Court ruling suggesting that opponents of restrictions must demonstrate that a law limits abortion in all cases.

If the Supreme Court reverses the appellate court, other states could be free to pass legislation similar to New Hampshire's.

The administration is also defending a 2003 federal ban on what opponents call "partial-birth" abortions, which does not have an exception for the health of the pregnant woman. The ban has not taken effect because three district courts ruled it unconstitutional and it is on appeal in three circuit courts. The Supreme Court in 2000 rejected a Nebraska ban on the procedure because it lacked a health exemption.

Clement, in his filing yesterday, said the Supreme Court's decision in the New Hampshire case "may have direct relevance" to the "partial-birth" case.