(Reuters) — A majority of U.S. Supreme Court justices on Wednesday signaled support for a Muslim woman who filed a lawsuit after she was denied a job at an Abercrombie & Fitch Co. clothing store in Oklahoma because she wore a head scarf for religious reasons.

The nine justices heard a one-hour argument in an appeal brought by the U.S. Equal Employment Opportunity Commission, which sued the company on behalf of Samantha Elauf. She was denied a sales job in 2008 at an Abercrombie Kids store in Tulsa when she was 17.

The case involving alleged workplace discrimination against a young Muslim woman in the American heartland comes before the top U.S. court at a time when some Western nations are struggling with culture clashes relating to accommodating local Islamic populations. The United States has not, however, faced the same tensions as some European countries, including France.

The legal question is whether Ms. Elauf was required to ask for a religious accommodation in order for the company to be sued under the 1964 Civil Rights Act, which, among other things, bans employment discrimination based on religious beliefs and practices.

Ms. Elauf was wearing a head scarf, or hijab, at the job interview but did not specifically say that, as a Muslim, she wanted the company to give her a religious accommodation.

The company denied Ms. Elauf the job on the grounds that wearing the scarf violated its "look policy" for members of the sales staff, a policy intended to promote the brand's East Coast collegiate image.

During the oral argument, it appeared the court's four liberal justices are likely to vote in Ms. Elauf's favor. At least one of the court's conservatives, Justice Samuel Alito, seems set to follow suit.

Senior liberal Justice Ruth Bader Ginsburg criticized the company's argument that its decision not to hire her was based on the "look policy" and that whether or not Ms. Elauf was a Muslim was irrelevant.

Justice Ginsburg said the civil rights law requires certain people to be treated differently to other applicants if they have a religious requirement.

"They don't have to accommodate a baseball cap. They do have to accommodate a yarmulke," Justice Ginsburg said, in a reference to the cap worn by some Jewish men.

Justice Alito said employers like Abercrombie could easily find out if prospective employees need a religious accommodation by simply asking if they are able to abide by work rules.

He noted that Abercrombie had assumed Ms. Elauf would wear the head scarf every day simply because she wore it at the interview. "Maybe she just had a bad hair day," Justice Alito said.

Other conservative justices were more skeptical about the government's arguments.

Chief Justice John Roberts speculated that putting the burden on the employee to assess whether a religious accommodation is needed "may promote stereotypes to a far greater degree" by requiring interviewers to inquire about applicants' religious beliefs.

Muslim groups said in a friend-of-the-court brief in support of Ms. Elauf that employment discrimination against Muslims is widespread in the United States. Often, the act of a woman wearing a head scarf is what triggers the discrimination, according to the brief. The EEOC has reported that Muslims file more employment claims about discrimination and the failure to provide religious accommodations than any other religious group.

Groups representing Christians, Jews and Sikhs also filed court papers backing Ms. Elauf.

Abercrombie has faced other employee lawsuits, including one in which it agreed in 2004 to pay $40 million to several thousand minority and female plaintiffs who had accused the company of discrimination.

A ruling is due by the end of June.

The case is EEOC v. Abercrombie & Fitch, U.S. Supreme Court, No. 14-86.