The Supreme Court, which last year gave lawyers the right to advertise, was asked yesterday to overturn another traditional tenet of the profession and allow them to solicit clients the way stockbrokers and bankers do.

In separate and very different cases, lawyers from Ohio and South Carolina argued before the court that the ban on soliciting clients violates attorneys' First Amendment right of free speech.

But a friend-of-the-court brief submitted by the American Bar Association said allowing lawyers to solicit clients -- generally known as "ambulance chasing" -- "would pose the danger that subtle forms of coercion and undue influence could be brought to hear to encourage unsophisticated persons to hire particular attorneys."

Another friend-of-the-court brief, filed by Ralph Nader's Public Citizens Inc. and the National Resource Center for Consumers of Legal Services, two groups seeking reform of the legal system, said the current bans on soliciting "constitute a disservice" because they don't distinguish between "helpful and harmful" solicitations.

Both cases before the court were brought by lawyers who had been disciplined for soliciting clients by state supreme courts, which had the authority to regulate the conduct of lawyers in the state. But that is about the only thing the cases have in common.

One involves Edna Smith, a South Carolina attorney who takes cases for the American Civil Liberties Union. She offered by letter to represent Marietta Williams, a welfare mother from Aiken, S. C., who was sterilized after the birth of her third child by a doctor who refused to deliver the baby if she didn't agree to the procedure.

Williams decided not to sue the doctor, Clovis H. Pierce, but the state bar association charged Smith with soliciting a client and publicly reprimanded her.

"The state's interest in preventing the stirring up of litigation is especially great where, as here, the litigation would interfere with established relations" between Williams and her doctor, South Carolina said in its brief to the high court.

Assistant Attorney General Richard B. Kale Jr. argued that the letter from Smith is not protected by the First Amendment, and that people ought to be allowed to decide whether to file a lawsuit without being pressured by a lawyer.

Ray P. McClain, representing Smith, said the letter was merely designed to make sure that Williams understood her rights.

Moreover, he said in answer to a question by Chief Justice Warren E. Burger, a letter is different from a face-to-face confrontation and should be protected by the First Amendment in the same way the court held that advertising by lawyers is.

In the second case, Cleveland lawyer Albert Ohralik was suspended indefinitely from the practice of law after being charged with persuading two women to let him take their cases after a traffic accident.

They later fired him as their attorney and brought charges before the Board of Commissioners on Grievances and Discipline.

His attorney, Eugene Gressman, argued that Ohralik was acting "in the highest traditions of the profession" by offering legal help to people who needed it.

He cited the Supreme Court decision on advertising and said the legal profession's ban on soliciting clients originated in England, where barristers didn't want to compete with each other and act "as ordinary tradesmen."

But John R. Welch, representing the Ohio Bar Association, said the ban protects the public "from the harm that can come from public solicitation by attorneys."