Citing constitutional objections to a federal court order, President Reagan yesterday vetoed a $20 million appropriation designed to help Chicago move forward with a federally mandated school desgregation plan, although he said he did so "reluctantly."

Congress appropriated the money to end an impasse between the administration and a U.S. district court over federal financial aid for the Chicago plan. However, the president said in effect that the constitutional questions raised by the order are so important that he does not want the impasse ended until the higher courts rule.

The $20 million had been provided by Congress after Judge Milton I. Shadur, declaring that the federal government was dragging its feet on what he viewed as a 1980 commitment to help Chicago fund the desegregation plan, ordered the United States to come up with a plan to provide some money.

In a June 30 ruling, Shadur said the government should draft a plan to provide a minimum of $14.6 million for the next school year, and up to $250 million over the next five years to help carry out the Chicago desegregation plan.

To make sure the money would be available, according to administration officials, Shadur blocked the Department of Education from distributing nearly $300 million for various nationwide educational programs. Education officials said the money included $250 million in unused student loan funds and an estimated $38 million to $50 million in other federal education funds.

The administration is appealing Shadur's order. An official said the position is that the 1980 desegregation agreement did not commit the federal government to specific spending but only to use its "best efforts" to fund the plan.

And, the administration contends, Shadur went far beyond his constitutional authority in ordering the student loan and other funds which were appropriated by Congress for specific purposes, to be set aside for possible use for the Chicago desegregation plan, which is not the purpose for which Congress voted the money.

The provision of $20 million by Congress was an attempt to ease the conflict between the administration and court and, by providing enough money for the plan for the coming school year, induce Shadur to release the frozen $300 million.

However, the president said in his veto message, which was issued from El Paso, where he was traveling, that he wanted the higher courts to decide the constitutional issue of whether the judge had the power to order funds set aside for the Chicago plan that were appropriated for a different purpose.

"Congress hoped by the passage of this legislation to induce the court to release the funds that were impounded by the court," Reagan said. "But I believe that the better course is to seek swift reversal of the district court's order."

He contended that the Constitution "does not permit the judiciary to determine spending priorities or to reallocate funds appropriated by Congress" or "to withhold millions of dollars worth of unrelated and necessary education programs in order to enforce its orders."

Therefore, he said, he was reluctantly vetoing the bill, but if higher courts upheld Shadur's order for the federal government to help fund the Chicago plan, he would do so.