Conservative judges on the US supreme court sharply challenged lawyers attempting to bring the biggest sex discrimination case in history as a key hearing on the case got underway in Washington.

The court's justices are set to decide by June whether lawyers representing potentially more than a million women employed by Walmart can bring a class-action sex-discrimination lawsuit against the retail giant. Their decision looks set to redefine discrimination cases in the US.

Justice Anthony Kennedy, a moderate conservative, and Justice Antonin Scalia, a conservative judge, questioned the basis of the case. Kennedy said Walmart's record on pay and promotion was better than the US average. "I'm just not sure what the unlawful policy is," he said.

The potentially liability in the case could reach billions of dollars. The suit began nearly 10 years ago when it was originally filed on behalf of employee Betty Dukes and five of her co-workers. Walmart is appealing an earlier court's decision to let the case go to trial.

Joseph Sellers, a lawyer representing the women, said Walmart, owner of Asda in the UK, has a corporate culture that stereotypes women and that has led to discrimination in pay and promotion.

"These decisions are informed by the values the company provides," Sellers said. He added that earlier courts had been persuaded by this argument and a wealth of statistical evidence that there was a class action case to be answered.

Scalia attacked Sellers position, saying he was "whipsawed" by the argument that either individual managers are on their own, "or else a strong corporate culture tells them what to do". "Which is it?" he asked.

Legal expert Stuart Slotnick of New York law firm Buchanan Ingersoll & Rooney said it was too early to tell which way the judges would vote but it was clear that the statistical element in the case was "causing concerns".

"Statistics alone seem to be troubling for the courts," he said.

"There needs to be other evidence than a mathematical analysis of pay scales." He said evidence, such as testimony from employees about a sexist corporate culture or a policy of discrimination, would bolster the case.

The plaintiffs were given some support by justice Ruth Bader Ginsburg, an expert on sex discrimination law.

She said the issue being decided was whether the case has enough evidence to proceed and not if discrimination could be immediately proven. "We're talking about getting a foot in the door," Ginsburg said.

Wal-Mart denies discrimination.

Lawyer Theodore Boutrous Jr told the court: "There is absolutely no way there can be a fair process."

He said it was impossible for the company to defend its treatment of such a massive number of people when they worked at thousands of different stores and in many different jobs.

Outside the crowd protesters gathered shouting "Fair pay now" and carrying signs such as "Stop discounting the women of Wal-Mart" and "The women of Wal-Mart are not worthless"."