Secretary of State George P. Shultz said last night that the Reagan administration seeks to advance U.S. relations with China despite "our close unofficial relationship" with Taiwan.

Shultz spoke on U.S. policies in Asia to a World Affairs Council dinner in San Francisco honoring special Mideast negotiator Philip C. Habib. The speech came a week after new blasts from Peking regarding Washington's stand on Taiwan.

Apparently alluding to this controversy, Shultz said frustrations and problems in Sino-American relations are "inevitable."

In his address, as prepared for delivery, he added, "We believe that these problems can be managed and that the community of interests that promises further progress is real. Our relationship with China has brought tangible results and can be a potent force for stability in the future of the region."

The high value placed on Sino-American relations was balanced by Shultz's description of the unofficial U.S. relations with Taiwan as "close," a word not often used in this connection.

Shultz also spoke of U.S. relations with Japan, calling the attitude of Prime Minister Yasuhiro Nakasone on trade issues "refreshingly operational," thus conveying a positive U.S. response to recent Japanese actions in that area.

Shultz also spoke positively of Japan's "commitment to undertake broader responsibilities for its own defense."

Shultz said the United States will continue to press Japan for greater efforts in the trade and defense fields.

The address, Shultz's most complete statement of Asian policy since he became secretary of state, praised Asian nations for economic advances that have led the world in growth. He noted that U.S. trade with Asian nations is greater than that with any other region and that the region accounts for one-sixth of total world trade.

Such achievements are the result of "a commitment to hard work, a willingness to sacrifice immediate benefits for future growth, and generally sound policies of economic management," he said.

One purpose of the speech was to reassure Asians that "the United States will remain a Pacific power," balancing the Soviet Union's increasing military strength in the area.

While asking Japan and others to do more in the defense field, Shultz said the U.S. goal "is to gain added strength together, not to decrease our own efforts . . . . Although specific tasks may change, our overall responsibilities will not be diminished in importance nor shifted to others."