The International Olympic Committee recognized the Olympic committee of the People's Republic of China yesterday but refused to expel Taiwan, opening the door for both states to compete in the 1980 Olympics in Moscow.

Although serious obstacles remain, an American member of the IOC who was reached at the meeting in Montevideo, Uruguay, said he was optimistic that both parties would accept the committee's terms within a month.

Delegations from Peking and Taipei reportedly made substantial compromises. Committee member Douglas Roby of Ann Arbor, Mich., said Taiwan accepted the IOC proposal, which left open problems relating to the names, anthems and flags under which the two representations would compete.

"I think they're going to make a settlement," Roby said. "I'm very happy, although it'll probably take a month to iron out the details."

The IOC will meet again during the Pan American Games in San Juan, Puerto Rico, in June. By then, the committee hopes to settle the issue of Chinese participation in the Olympics.

China applied in 1975 to participate in the Olympics after a 17-year absence. But Peking's sports federation has insisted that Taiwan be treated as a part of China and not have its own representative. The Taiwanese have demanded that they be recognized as the sole representative of China.

Delegates said the decision was reached after two days of difficult negotiations. IOC President Lord Killanin told a press conference in Montevideo after the vote, "Remarkable progress has been made in the last few days. I think the doors are open for what I have always had as my aims.

"If the door is slammed by either side, it will not be my fault."

Olympic sources and other observers said Taiwan's apparent acceptance of the IOC proposal, which passed by a 36-28 vote, and the fact that China did not reject it outright, indicated Peking may be moving from its insistence that Taiwan be excluded from international sports bodies recognizing the mainland government.

News services reported that Song Zhong, the secretary general of the Chinese committee and head of the Peking delegation at Montevideo, issued a statement saying the IOC resolution was "not acceptable to us in its present content."

The one point that appeared to upset the Chinese was the name given Taiwan in the resolution-the Chinese Olympic Committee located in Taiwan.

"The Taiwan sport organization may remain in the IOC under the name of the Chinese Taiwan Olympic Committee," Song's statement said.

Observers felt the language of the Peking statement gave the two nations room to negotiate. Roby said, "I think we can get around that."

There had been some concern as well as to the position of the Soviet Union, the host country for the 1980 Summer Olympics. The Soviets preferred to have Peking represented, and observers believed that they would vote against allowing Taiwan to continue in the IOC if mainland China was admitted.

On the other hand, as the host country, the Soviets were reluctant to take action against another IOC member and be accused of making politics an issue. The Soviets reportedly voted with the majority yesterday.