John B. (Jack) Kelly Jr., recently elected president of the United States Olympic Committee and a leading advocate of amateur sports for more than 30 years, died Saturday while jogging near his Center City home in Philadelphia. He was 57 years old.

A preliminary autopsy report yesterday showed that Mr. Kelly, a member of one of Philadelphia's most prominent families and a former City Councilman, had died of natural causes.

Seven hours after Mr. Kelly's death, the police said, his brother-in-law, Eugene Conlan, also 57, was found dead under similiar circumstances.

William E. Simon, former Treasury Secretary and Mr. Kelly's predecessor in the Olympic post, said yesterday by telephone from Nassau in the Bahamas, where he was vacationing: ''He was an irreplacable asset to the Olympic movement.'' Mr. Simon added that he was stunned by the news, saying: ''Jack and I have been personal friends and colleagues for 20 years. He always prided himself in being in magnificant shape.''

Was Outstanding Oarsman

Mr. Kelly, formerly an outstanding oarsman, was elected to a four-year term as U.S.O.C. president last February. At about the same time, George D. Miller was named secretary general, succeeding F. Don Miller. F. Don Miller (the two are not related) is executive director of the new United States Olympic Foundation. which overees a fund of more than $1 million to further amateur athletics.

''It's a loss to amateur sports in our country,'' he said. ''Jack has been identified with amateur sports all of his life and had looked forward with great anticipation to serving as president.''

George Miller said from Colorado Springs, ''The U.S.O.C. would have made tremendous progress in the next four years under him.''

John Brendon Kelly Jr., a graduate of the University of Pennsylvania, was born in Philadelphia. Active in athletics since he was a boy, he won the 1947 Sullivan Award as the nation's outstanding amateur athlete.

Father Won 3 Gold Medals

The Olympic feat Mr. Kelly wanted most to duplicate was that of his father, Jack Kelly Sr., who won a total of three gold medals in sculling in 1920 and 1924. Mr. Kelly competed in four Olympics from 1948 to 1960, winning a bronze medal in the 1956 Games at Melbourne, Australia.

He won the Diamond Sculls in 1949 and 1950 at the Royal Henley Regatta. The British had banned his father from the race purportedly because he worked with his hands.

During the 1960 Olympics in Rome, where he had a reunion with his sister Grace, the late Princess of Monaco, Mr. Kelly had this to say on whether rowing was a totally amateur sport: ''The presumption is incorrect. It exposes the entire fallacy of the amateur code. As soon as the rules are enforced to the letter of the law, two-thirds of the athletes are guilty of some violation and therefore perjure themselves when they take the Olympic oath.

''One rule for oarsmen is that none is permitted to work for money in or around boats. I violated that when I worked as a lifeguard. After I won the Diamond Sculls, the City of Philadelphia presented me with a magnificent trophy that must have cost $2,000. The rules put a $50 price limit on trophies.

''If I could infringe on the rules against taking a month off to travel or to train, it was because I had a rich father. Virtually no other athlete is that lucky. The point I'm reaching for in my little crusade is to modernize a code that goes back to the Gay Nineties' code that ostracized my father.''

Olympic rules have since been modernized, particularly in regard to expenses and training centers for athletes.

Sought More Women's Events

Mr. Kelly, who was described by an Olympic official ''as the athlete's best friend,'' was elected in 1970 as president of the Metropolitan Amateur Athletic Union. He served the Olympic movement in various capacities, leading to his assumption of the U.S.O.C. presidency, which is a policy-making office. Since his election, he had explored ideas for adding events for women athletes.

Mr. Kelly recently relinquished control of the family brickwork company.

The U.S.O.C. constitution does not provide for a line of succession in event of death. The president is elected by the 16-member executive board, which is expected to meet soon to chose a successor. Until one is chosen, according to Robert Paul Jr., a spokesman, Robert H. Hemlick of Des Moines, the committee's first vice president, will serve as interim president.

Mr. Kelly is survived by his wife, the former Sandra Lee Worley; a son, John B. 3d, and five daughters from a previous marriage; his mother, Margaret, and two sisters.

Funeral services are scheduled for Saturday at the Basilica of Saints Peter and Paul in Philadelphia.

John Kelly (1927)