Treasury Secretary Michael Blumenthal arrived here tonight on a week-long visit to establish the framework of closer economic relations with the Peoples Republic of China.

Heading a party of 16 government officials, Blumenthal predicted that the United States and China would build "a permanent relationship" that would have "obviously substantial benefits" for both countries.

Blumenthal is the highest American official to visit Peking since normalization of relations was announced last Dec. 15. His mission follows closely on Vice Premier Teng Hsiao-ping's series of meetings with President Carter in Washington last month.

The trip comes at a time of increased tension in Asia caused by China's invasion of Vietnam and the combat in northern Vietnam now in its seventh day.

Blumenthal's arrival coincided with that of Gov. Jay Hammond of Alaska, who plans a four-day stay as part of a "friendship and commerce mission" to several Asian nations. Another arrival signaling Peking's interest in increased trade with the West was that of British Industry Minister Eric Varley, who was to have talks aimed at a Sino-British trade pact.

During a briefing on the flight here Blumenthal hinted that the Carter-Teng meeting in Washington had yielded a political decision to solve the knotty question of financial claims that the two countries have against each other. This issue has been assigned top priority by both sides.

China does not accept the legitimacy of $196.8 million in claims by American citizens and companies that have been certified by an American claims commission. But Blumenthal said that "both sides want to settle this question on a realistic, not a legalistic basis."

There exist, as a potential offset to the U.S. claims, $80.5 million in Chinese assets frozen in the United States. But American officials say that a large proportion of these assets, for one reason or another, may never be available for liquidation in a "package deal" that would result in an acceptable partial settlement of the large American claims.

Officials suggested therefore that China, without admitting any error in seizing the American assets in 1949 when the Communists came to power, might be willing to "sweeten the pot" with a direct cash contribution that would make an overall settlement acceptable to Congress.

A representative of Jardine, Matheson and Co. announced here that agreement had been reached to allow American and Chinese merchant ships to call at each other's ports without a final resolution of the claims and assets issue.

The official said a Justice Department interpretation of a law passed three years ago allowed a loophole that would protect the ships from being attached and perhaps even open the way for air transport between the two countries earlier than was expected.

Another residual of the Carter-Teng talks will be the activation here this week, Blumenthal said, of a joint economic commission to supervise and smooth the way to broad, bilateral economic relationships.

At the same time, Blumenthal said three working groups will be set up this week to deal with banking and financial problems, trade, and taxation. These will be chaired for the United States by Under Secretary of Treasury Anthony Solomon, Assistant Secretary of State Julius Katz, and Emil Sunley, a Treasury aide on tax policy.

Although Blumenthal said the first priority of his trip is to try to settle the claims-assets problem he made clear that a longer-range goal is for the United States and China -- after a 30-year separation -- to learn more about each other.

"We need to learn how the Chinese economy functions, and we must explain to them about the American economy, and also about the international economic situation," Blumenthal said.

Separately from the private claims question, there is the matter of U.S. official claims against China, including $26 million in old loans by the Export-Import Bank, a claim of $660,000 by the U.S. Postal Commission, and a claim in the millions for consular and other U.S. property taken over by the communists when they came to power,

The private claims issue will get priority, Blumenthal said, because without agreement on it nothing else can go forward. He then will turn his attention to a bilateral trade agreement.