Vice President Mondale today opened the first U.S. consulate in China in 30 years, paving the way for increased American contacts with the southern Chinese coast where the largest number of Chinese Americans trace their ancestry.

On the last full day of his week-long China trip, Mondale also announced plans for talks on regular airline service between China and the United States and stressed the need for continued improvement in Sino-American ties so that the relationship will not go sour.

Administration foreign policy aides called it Mondale's most successful overseas trip. U.S. Ambassador to Peking Leonard Woodcock said Chinese dismay at American delays in granting promised most-favored-nation trade benefits made Peking "extremely suspicious" of the trip, but Mondale's explanations of a delay caused by a congressional logjam won the Chinese over.

"Normalization as you well know can mean an awful lot or it can mean very little," Mondale told a group of American businessmen based in Asia. "It can be a new excuse for grinding bureaucratic wheels or it can be a framework for cooperation for years to come."

Mondale opened the new consulate on the 11th floor of Canton's Dong Fang Hotel, the usual resting spot for American tourists stopping here. The new consul general, Richard Williams, and a staff of four or five will live and work there until permanent quarters can be found.

Administration officials see the opening of the consulate, as well as the airline talks and cultural and hydroelectric agreements signed in Peking, as signs of the steady progress needed to make the relationship work.

They describe Mondale's speech at Peking University Monday, which was broadcast throughout China, as the first detailed justification for improved Sino-American relations voiced by an American leader, and as an attempt to anticipate future attacks upon the relationship from domestic critics in the United States and China.

China's effort to modernize its economy is crucial to American security.

"If they don't make it, they will be the first underdeveloped nuclear power to fail in modernizing, and what does that do?" one longtime observer here asked.

Presidents Nixon and Ford, and for much of his term President Carter, have been unable to lay out a general case for becoming friends with Peking because of the political difficulties of discussing the Taiwan issue. With Taiwan apparently still enjoying military security and economic health with no formal U.S. ties since early this year, administration aides say they can now push for closer ties with Peking.

Williams, 49, the new counsul general, has been in the State Department 20 years and has served in both Taiwan and Hong Kong. He speaks the Chinese national language, called Mandarin or pu tong hua. Today he delivered a short address, saying he was honored to open the office. He spoke in English, Mandarin and Cantonese, although he says he is not yet fluent in the local dialect. His wife, Jane, is a naturalized American, born in China, and speaks Mandarin.

The Canton consulate will begin assuming much of the burden of requests by Chinese to visit relatives in the United States. Mondale got some sense of the close family ties between China and America in this area when he visited the Huashan commune outside Canton today and found a production brigade of 2,600 people, 2,100 of whom have relatives in the United States.

This is the part of China where thousands of laborers were recruited to build America's transcontinental railroad in the mid-19th century. The laborers in turn brought their relatives to the United States. Throughout the area are scattered large houses financed by generous relatives in San Francisco, Seattle and other U.S. cities, often with the benefactor's picture displayed prominently in a front hall.

Mondale said today Chinese and American negotiators were working on a consular convention that would not only provide for the already agreed-upon consulates in Canton and Shanghai, and in Houston and San Francisco, but allow others in both countries as well. The last U.S. Canton consulate, on Shamien Island here, was closed by the Communists in 1950. Officials here said the building is apparently now used by the local foreign affairs bureau. No one here today could remember the name of the last U.S. cousul general in Canton.

One sign of the lessening of the Taiwan problem was the presence today of Robert Parker, president of the American Chamber of Commerce in Taipei and an outspoken critic of President Carter's decision to cut relations with the Nationalist Chinese island. Parker made his first trip to China this week to represent Taiwan's American businessmen at an annual gathering of American chambers in Aisa, also addressed by Mondale at their meeting in Jakarta last year.

Parker said the Taiwan chamber first declined to send a representative, then changed its mind when reports circulated that it had been barred from entering the People's Republic.

Parker's Chinese friends on Taiwan "said only two things, don't let them trick you and take lots of pictures," Parker said. At the lunch with Mondale, he asked if the U.S. decision to continue only an informal airline agreement with Taiwan would hurt air service to the island, and was assured it would not.

U.S. officials said they expect some difficulty winning Chinese approval for more than one U.S. airline, Pan Am, Peking's favorite, to fly into China, but the Americans will insist on this point in talks beginning in September.

[Mondale arrived in Hong Kong Saturday morning, news agencies reported.]

In summing up the trip, one Mondale aide said that in the past the Chinese had suspected that Washington dealt with them only as a "derivative of our relations with the Soviet Union," but now seemed convinced and happy that Washington was dealing with "China as China" and doing everything possible to promote Chinese economic growth as a stabilizing influence in the world.