Secretary of State Cyrus Vance and Chinese Vice Premier Teng Hsiao-ping held what they called "useful and serious" talks on improving relations today, but there was no indication of a breakthrough on the key issue of Taiwan.

In the face of American displays of reluctance to cut its ties with the Nationalist Chinese island, the participant of an official of Teng's stature and the sumptuous dinner he gave for Vance tonight suggest that Peking has decided to continue dealing with Washington even though progress toware normalization of relations is slow.

State Department spokesman Hodding Carter III told reporters after the 2 1/2 hours of afternoon talks and the dinner at the old impoerial pleasure dome called the Summer Place:

"I wouldn't want to go so far as to suggest there has been some kind of massive, innovative change . . . I think it has been a good exchange today."

Despite the good feelings and banter reported at the private dinner for Vance and his staff, it appeared that after three days of conversations the two sides had merely laid out their respective positions on the offshore island of Taiwan where their interests clash.

Washington officials have often said in the past that they need some sign that China will not try to retake its island province by force. The Chinese have said that the United States must cut its military and political ties with Taiwan and leave decisions about the island's future to Peking.

The Taiwan Central News Agency reported that Richard Holbrooke, U.S. assistant secretary of state for East Asian and Pacific affairs, will arrive in Taipei Friday to brief Nationalist leaders on Vance's visit to Peking, Reuter reported.

At tonight's dinner, which was closed to the press, Teng gave a short toast in which he called the talks "explicit and very candid," Carter said. Carter quoted Teng as saying: "They are of great use. our view is that we should move forward toward full mobilization of relations."

According to Carter, Vance replied in his toast: "I believe we have had useful and helpful talks" with both Teng and Foreign Minister Huang Hua. "We believe they have been candid and very useful and very hopeful. I also look forward to the movement forward of the relations of our two nations in accordance with the principles of the Shanghai communique," the joint statement issued by president Nixon and Premier Chou En-lai in 1972.

We believe this visit to Peking is an important step toward progress along that road," he added.

The day produced a virtuouso performance by Teng, returning to a major public role in Chinese foreign policy after an unprecedent second come back from political oblivion. Carter said Teng referred at the banquet to his life during the last 18 months, when he was in forced retirement because of a political purge.

The U.S. spokesman refused to say exactly what Teng told his guests, holding to the rule laid down during this trip barring any discussion with the press of any specific matters from the private talks.

After two days in which the Chinese side was represented by Foreign Minister Huang, Teng joined the talks this afternoon and gave them new significance because of his position in the ruling Politburo. He shook hands with almost all the American reporters standing in a lobby of the Great Hall of the People waiting for the talks of begin.

According to Carter, Teng did about two-thirds of the talking as the afternoon conversations range over international and bilateral matters, including Taiwan.

The talks ran an hour longer than scheduled, forcing the American party to rush to the beautiful Summer Palace park of lakes and ornate Ching dynasty buildings for a boat ride and dinner.

Much of the Summer Palace was burned down by French and British troops in 1860, and it was damaged again in 1900 by troops of a Western expeditionary force, which included Americans, trying to put down the Boxer Rebellion. Chinese officials escorting Americans around assured them they hold no grudge against the American people, and the atmosphere as Teng appeared for the dinner at the Listen to the Oriole restaurant was jovial.

Carter said Teng traded jokes with his American guests during the dinner. It included swee-and-sour carp, sharkfin soup, duck cutlets, amond float and huge peaches for dessert.

The New China New Agency today published the full text of Teng's speech last week at the conclusion of the 11th national party Congress . Teng urged that the campaign against his old enemies - the radical "Gang of Four" led by Chiang Ching, widow of Chairman Mao Tse-tung - be carried through "to the finish."

In remarks that were largely inspirational, he exhorted Chinese people to talk less and work more, although he also called for more debate within the party and recalled that Mao had said, "Say all you know and say it without reserve."

He called for a objective search for truth, saying: "The minimum requirement for a Communist is to be an honest person . . . We must reject flashiness without substance and every sort of boasting . . . We must be steadfast and dedicated."