The US is "making progress" towards more reductions in abortions, President George W Bush has told pro-life campaigners rallying in Washington.
Both sides in the argument mark the Roe v Wade ruling each year
Mr Bush did not go to the demonstration but made a speech by telephone, saying abortion opponents had to show others of "the rightness of our cause".
Many think changes at the Supreme Court would bring revisions to abortion law.
Pro-choice groups also rallied, 32 years after the landmark Roe v Wade court ruling legalised abortion.
President Bush tightened access to abortion during his first term, banning some late-term abortions and offering legal protection to doctors and hospitals unwilling to carry out terminations.
On Monday, Mr Bush said, in what was described as a passionate speech, that "the strong have a duty to protect the weak".
"The America of our dreams, where every child welcomed in law... and protected in law may still be some ways away," Mr Bush said.
The "culture of life" requires more than simply legislation, he added, saying: "We need, most of all, to change hearts.
"And that is what we're doing, seeking common ground where possible, and persuading increasing numbers of our fellow citizens of the rightness of our cause."
The prospect that Mr Bush may have the chance to nominate one or more Supreme Court justices during his second term has electrified the abortion debate, correspondents say.
Several of the court's nine serving justices are over 70. One, Chief Justice William Rehnquist, is 80 and suffering from thyroid cancer.
Some Bush voters expect tougher action against abortion
Randall Terry, founder of pro-life organisation Operation Rescue, told the Associated Press news agency that Mr Bush has an "ethical obligation to protect the unborn".
"His staff must thoroughly investigate any possible appointee, and if they are not unalterably committed to overturning Roe v Wade, they must be dismissed from consideration," Mr Terry said on Saturday.
Pro-choice groups say abortion rights are being eroded in the US.
Vicki Saporta, president of the National Abortion Federation, said her fears about future judicial appointments were tempered by polls indicating most Americans do not want Roe v Wade overturned
"We shouldn't think that the positions we've taken are not just and moral," she told AP.
Ms Saporta said her organisation wanted to ensure women got "correct medical and scientific information".