(CNN) -- The city of New Haven, Connecticut, will promote 14 firefighters who were involved in a workplace discrimination case that worked its way to the U.S. Supreme Court.

The firefighters were among the New Haven 20 -- one Hispanic and 19 white firefighters -- who fought the city after it threw out the results of a 2003 firefighter promotion exam that left too few minorities qualified for promotions.

A U.S. District Court issued a judgment finding the city violated the civil rights of a group of the white firefighters when it threw out the exams in 2004, according to Jessica Mayorga, city spokeswoman. The Tuesday decision follows a court action by seven black New Haven firefighters seeking to delay the promotions.

"Yesterday, the court entered an order that provides the City of New Haven with the legal sanction necessary to move forward and promote the fourteen plaintiffs in the Ricci case entitled to promotions," the city said in a statement. "As a result, we intend to do so as soon as practicable."

The firefighters will be promoted to either lieutenant or captain.

Mayorga said the other six involved in the lawsuit were not eligible for promotions that were available at the time the exams were given. She said the court's order only addresses 14 of the 20 plaintiffs. If the exams had been certified in 2004, the other six plaintiffs would not have been promoted.

The case was the center of attention during the Supreme Court confirmation hearings of now-Justice Sonia Sotomayor, who was on the 2nd Circuit Court of Appeals that backed the city in the case. The U.S. Supreme Court eventually overturned the appeals court ruling 5-4 earlier this year when the justices ruled that the city improperly threw out the results of the promotion exams.

Key plaintiff Frank Ricci and others took promotion exams in 2003 for lieutenant and captain positions that had become available in Connecticut's second-largest city.

New Haven's personnel department had contracted with a private firm to design the exams.

When the results came back, however, city lawyers expressed concern about the results because none of the black firefighters and only one Latino who took the exam scored high enough to be promoted.

The city said that under a federal civil rights law known as Title VII, employers must ban actions such as promotion tests that would have a "disparate impact" on a protected class, such as a specified race or gender. The group of firefighters, claiming they were wronged by the city's action, then sued, calling themselves the "New Haven 20."