The Supreme Court yesterday ordered immediate implementation of a court-ordered school desegregation plan for Columbus, Ohio, that would require busing 37,000 of that city's 89,000 pupils.

The court had cleared the way for carrying out the desegregation plan in a July 2 decision that, together with a companion decision in a Dayton, Ohio, case, reaffirmed a landmark 1973 decision that has served as a foundation for school desegregation plans in northern cities.

Under court rules, compliance with a high court decision may be postponed if the defendant appeals during a 25-day period, which the Columbus board of education did Thursday.

The Columbus board filed for rehearing of the case, which court officials said would have delayed compliance until after the start of the 1979-80 school year.

The full court yesterday vacated a stay of the busing plan ordered last Aug. 11 by Justice William H. Rehnquist and ordered immediate implementation of the desegregation plan.

Rehnquist and Justice Harry A. Blackmun took no part in today's decision.

Meanwhile in San Diego, a Superior Court judge told that city's Unified School District it could continue with the nation's second-largest all-voluntary integration plan (behind Philadelphia) because the two-year-old plan had made "steady progress" and with little or no white flight.

Plaintiffs in the 12-year-old class-action suit on behalf of children in segregated schools vowed to appeal.