China recently has canceled $1.5 billion worth of contracts with Japan and is falling behind in other financial obligations as Peking reconsiders its headlong rush toward modernization.

The souring business relationship has upset the Japanese government, which fears that the disenchantment could spread and lead to a deterioration of the good relations patiently built up with China since the two countries officially became friends again in 1972.

Since mid-January, Chinese officials have notified some of Japan's biggest companies that the contracts worth roughly $1.5 billion have been canceled. They include a huge steel plant near Shanghai and several petrochemical plants.

In addition, it appears that China is falling behind in its commitments under a large 1978 two-way trade agreement that was to be the centerpiece of economic relations between the two Asian powers for the rest of this century. China already has slipped back on its oil promises.

The contract cancellations have stunned Japanese companies, which are worried about compensation for production already under way.

To register its concern, the Japanese Foreign Ministry today sent its top economic trouble shooter, Saburo Okita, to Peking, with a team of other officials who hope to find out what is happening there.

News reports here have said that Okita will warn the Chinese government that the cancellation notices could have a severe effect on the two countries' future relations.

Late in 1980, China began issuing notices that some major projects would be postponed and delayed, but there were no hints of out-right cancellations. The moves were presumed to reflect a new Chinese strategy of slowing down its rush toward heavy industries and turning to light industries and more consumer goods to satisfy domestic demand.

Then in January the cancellation notices began flowing out of the China National Technical Import Corp., which had made contracts with several Japanese companies. The notices contained little to explain the cancellations.

"It was so sudden, and we were so surprised," said Kazuhiko Hamano, notice cancelling a $425 million hot strip steel mill it was building as part of the huge Baoshan steel works near Shanghai.

There was more puzzlement when China ordered home about 100 apprentices who had been sent to study Mitsubishi's methods in Japan.

A Mitsubishi spokesman said today the company has no official position yet on what compensation it will seek and wants to get more details from Chinese officials.

The compensation issue could become difficult. If the Chinese government refuses compensation, the Japanese companies could collect export insurance payments from the Japanese government to cover some losses. That in turn could cause the government, under current law, to list China as a country not covered for future export insurance. That would severely restrict all Japanese trade with China.

An official of the Japanese Ministry of International Trade and Industry said today that without compensation some Japanese companies conceivably could go bankrupt, which would cause considerable "antagonism" between the two countries.

The official, Kazuichi Tamura, said that a lack of foreign exchange in China did not appear to be the problem, since Japan had provided both yen credits and export-import bank loans for the projects.

There are reports that China has agreed to compensate Japanese companies for any goods that have been shipped or that are still on the production line in Japan but wants to discuss the issue of compensation for all other contracted items.

There had been reports from China that the big steel plant had become widely unpopular because its construction consumed so much of the country's financial resources. The Chinese appear to have decided to reduce its scale sharply. Nippon Steel was to build two smelting furnaces. The company says China has served notice that it does not want the second furnace built and discussions must be held on some facets of the first furnace.

Cancellation of three large petrochemical in China of oil that was to be used for ethylene in the plants. There is not enough oil to supply the 300,000 tons of ethylene required, according to a Japanese official.