The administration has approved its first large-scale sale of military spare parts to Taiwan despite objections from the People's Republic of China, the State Department said yesterday.

State Department spokesman Dean Fischer said the mainland Chinese, who have opposed any U.S. military sales to Taiwan, were not notified in advance.

"We feel our position with the People's Republic of China has been consistent. We intend to continue defensive arms sales to Taiwan in a prudent manner," Fischer said.

Official sources described the sale of the spare parts, which are reported to be worth about $97 million, as unconnected with the pending and highly controversial question of selling the FX, an advanced jet fighter to Taiwan.

While opposing any sales to Taiwan as a matter of principle, China has reserved its fierce opposition for a high-profile sale such as that of sophisticated warplanes.

On several occasions, Chinese officials are reported to have threatened to downgrade diplomatic relations with Washington and halt development of military cooperation if such a major sale is made.

Senior administration officials had set an informal target date of the end of this year for a decision about the major Taiwan arms questions.

Fischer said yesterday that "no decision, even in principle" has been made on the jet fighter question. Other sources suggested that top-level deliberations on the issue are expected to take place early next year.

The Carter administration, in working out arrangements for normalization of Sino-American diplomatic relations late in l978, insisted on continuation of U.S. military sales to Taiwan. China did not agree that the sales could continue but went ahead with normalization knowing of the American view and intention.

President Reagan, who strongly supported Taiwan as a private citizen and presidential candidate, has been confronted with much stronger Chinese positions and expressions than those made known in the Carter administration.

While the State and Defense departments are reported to be cautious about any large-scale sale to Taiwan, the position of the White House staff and the president is in doubt.

Sale of the spare parts was described by Fischer as "in our view, a routine transaction." It came to public notice because it is the first such sale to Taiwan this year large enough to require congressional notification under arms export control legislation.