A federal court jury in Alexandria awarded $1,000 last night to a former Fairfax City firefighter who had claimed city officials demoted him because of his efforts to unionize the fire department there.

The jury deliberated more than four hours before awarding Dennis L. Rubin of Laurel $500 in compensatory damages and $500 in punitive damages, according to Fairfax City public information director Tom Welle.

Rubin, 30, who had sought $1 million in damages, said last night he was pleased with the outcome and "I hold a grudge against no one." He said he will seek reinstatement to his job as fire department lieutenant.

The award is to be paid by the city. The jury found that five individuals named in Rubin's suit were not liable in the case.

Former Fairfax City mayor Frederick W. Silverthorne, one of the five, said last night he was relieved by the verdict. "I certainly knew I was not guilty," he said. "But when something goes to a jury, they can believe you and they may not believe you."

Silverthorne and other city officials were accused of pressuring Rubin out of his $25,000-a-year job because of his activities in connection with the local chapter of the International Association of Firefighters, AFL-CIO. Rubin helped found the chapter and was its first president.

Attorney James W. Hopper, representing the city, denied the charge. He cited city records indicating that Rubin was demoted for violating standard operating procedures while directing firefighting operations at a blaze on Aug. 2, 1981, and for using profanity while directing firefighting operations on that occasion.

Shortly after his demotion, Rubin resigned.