The Japanese government today approved a defense budget increase of nearly 10 percent, a notable rise but less than Defense Agency officials had sought in their effort to satisfy American requests for a more active military program.

The increase of 9.7 percent over current spending emerged only after a strenuous internal debate between defense officials and the Ministry of Finance, which is trying to impose an austerity budget on the government in the coming fiscal year.

The increase will permit Japan to buy more jet fighters, patrol planes and ships -- many from the United States -- in the coming year.

But it appears to fall short of the spending pace that would enable Japan Japan to hasten implementation of a five-year defense program as requested by the American defense officials. The Japanese Defense Agency had wanted a 15 percent increase to satisfy that schedule, which will not be met unless there are more sizable increases in the next three years.

Despite this shortfall, the budget approved in a Cabinet meeting this morning represents a significant departure in handling military spending in this supposedly pacifist nation. It reflects the increasing tolerance of military expenditures.

Almost all other departments were held to increases of 7.5 percent, the general guideline established by the Ministry of Finance. This was the first time the Defense Agency had been exempted from the overall guidelines and prodefense officials regarded the move as important.

"This is a very significant political decision," said one government source. "It reflects the change in public opinion (about defense issues) and the new circumstances surrounding Japan, including the Soviet military buildup in this area."

Many political and business leaders have been pushing for greater defense expenditures in the past year, in part because of the Soviet naval and war-plane buildup in this region and in part as a response to the Soviet invasion of Afghanistan.

The United States had tried to encourage that movement without seeming to be insisting on specific levels of spending. The late prime minister Masayoshi Ohira in May promised President Carter that Japan would make significant defense increases this year.

U.S. officials had focused on a Japan Defense Agency plan to increase defense spending gradually by 1984 to reach a level equal to 1 percent of the country's gross national product. The current budget is equal to about 0.9 percent of GNP.

American officials had hoped Japan would accelerate that plan to reach the 1 percent level by 1983. To do that, the Defense Agency proposed starting this time with a 15 percent increase. It settled instead for 9.7 percent, which, with salary adjustments next spring would probably wind up at about 12 percent.

The document approved by the Cabinet today is still only a formal request and can be changed before formal legislation is sent to the parliament this fall. The Defense Agency is said to feel it will have a difficult time holding the Finance Ministry to the 9.7 percent compromise.

There are many signs that the Japanese are willing to accept a larger military establishment, despite a constitution that officially bans a defense force. The ruling liberal Democratic Party, with its large new majorities in Parliament, is in a good position to override the socialistic opposition and get whatever level of military expenditures it want.

But the new government of Prime Minister Zenko Suzuki also is wedded to the principle of reducing this country's dependence on national bonds to finance the government and has decreed the next fiscal year, beginning April 1, to be one of austerity.

Breaking the government-wide guideline to permit higher defense spending proved immediately unpopular today with some businessmen, who, concerned about deficit financing wanted the government to hold the line on all departments.

Tadashi Sasaki, chairman of the Japan Committee for Economic Development, registered his complaint today at the Finance Ministry and told reporters he found it "strange" that the government was exempting defense spending from the guidelines.

The ministry had reached the compromise agreement late last night with Defense Agency Director-General Joji Omura, who subsequently said he was not completely satisfied with the arrangement.

With the increase approved today, the Defense Agency would be spending about $10.9 billion in the fiscal year beginning in April.

Much of the new increase will be used to purchase E2C early warning aircraft, P3C Orion antisubmarine patrol planes, and F15 jet fighters from the United States. It will also be used to compensate the United States for some of the expenses of American bases here and to build more warships.