Prime Minister Yasuhiro Nakasone's government, seeking to avert a possible political backlash in the United States, today decided to boost its military spending budget in 1983 by 6.5 percent to a total of $11.7 billion. In so doing, Nakasone overrode a more tight-fisted proposal announced here on Saturday by the powerful Finance Ministry that limited spending increases to 5.1 percent.

In final negotiations here this week, Tokyo has been tightly wedged between the need to trim its huge budget deficits and strong demands by the United States that Japan shoulder a greater burden of defense spending in line with the country's economic clout.

Today's move, according to government officials and private defense analysts, reflected a bid by Nakasone to demonstrate Japan's good faith in expanding its military responsibilities.

But observers privately expressed concern that the 6.5 percent spending hike, which undershoots this year's 7.8 percent increase, may further amplify criticism of Tokyo's yen-pinching defense appropriations in the Reagan administration and on Capitol Hill. It will, they said, further delay the already glacial pace of Japan's plans to buy more of the antisubmarine patrol planes, warships, and other sophisticated military hardware needed to defend the country's airspace and sea lanes.

Adjusted for inflation, the real increase would be about 4 percent.

The Nakasone Cabinet was expected formally to endorse the country's overall 1983 budget for the fiscal year that begins April 1, at a special session here Thursday evening.

The 11th-hour decision to boost defense outlays came amid intense competition among rival government departments here seeking expanded shares of a $214 billion austerity spending program. In the coming year, the budget is set to grow by only 1.4 percent, the lowest year-to-year increase in nearly three decades.

Defense was given a clear priority over other appropriations, aides close to Nakasone said, because of a strong determination of the prime minister and top officials of the ruling Liberal Democratic Party to bolster ties with the United States, which have been badly strained over the issues of trade and defense. The move, observers said, reflected a high-level political decision to ease tensions between the two Pacific allies prior to Nakasone's scheduled visit to Washington in January for talks with President Reagan.

Officials here suggested privately that Nakasone may attempt to offset any disappointment over today's defense decision on Washington's part by guiding the government to a decision on a long-delayed proposal allowing Japan to transfer sophisticated military technology to the United States in advance of his visit next month.

Japanese Defense Agency officials indicated that the 1983 defense budget should bring Japan's military spending to 0.98 percent of its gross national product, compared to 0.93 percent in the current year. Once inflation is taken into account, the defense spending hike is expected to come to slightly over 4 percent, in real terms. This would outdistance the 3 percent increases contemplated by the United States' NATO allies, but fall considerably short of a roughly 6 percent commitment by the United States.

Speaking to reporters today, Foreign Minister Shintaro Abe stressed the need to strengthen ties with the United States. He indicated that Japan may be forced, in coming years, to abandon the 1 percent of GNP limit it imposes on its defense spending to meet its growing international responsiblities. Japan, he said, would implement a new five-year military plan designed to bolster the defense of its own sea lanes.

The United States has pressed Japan to take steps to defend sea lanes on its own to a distance of 1,000 nautical miles from its shores and the military experts from the two countries have embarked on a study to work out the details.

According to Tomohisa Sakanaka, a senior defense analyst, however, today's defense decision will make it "substantially impossible" to meet government weapons procurement plans outlined in the five-year program to begin next year.

For example, Japan's Defense Agency, which originally requested a 7.34 percent spending increase, will now only have funds available to buy 13 F15 jet fighters in 1983, compared to the 20 new planes it had expected. It will also be forced to settle for seven instead of 10 P3C antisubmarine patrol planes, and two, not three new destroyers.

"Increasingly tight fiscal conditions," Sakanaka said, "will make it more difficult to close the gap in weapons procurement" in later years.

Senior government officials admitted that the scaled-down defense budget would create delays in purchasing the front-line military hardware necessary to keep plans to expand defense capabilities on track. But they asserted the budget represented "the best possible efforts under the current circumstances" in which appropriations for most government departments were held below the current year's levels.

Officials said that 1983 defense outlays would result in more funds for military equipment, maintenance, and base construction than in 1982, despite the fact that this year's percentage increase was larger. This was possible, they said, because of a freeze on the wages of military personnel, in line with similar limits imposed on public workers here.

Reflecting the political tone of today's decision, officials pointed out that defense was overwhelmingly favored this week for a share in the $255 million in supplementary funds set aside by the government for all departments.

The decision was expected to touch off a storm of protest among Japan's Socialists, Communists and other opposition groups in parliament, which have demanded that more be spent on welfare payments and social security pensions.

A senior Defense Agency official, who did not want to be named, said the priority on defense spending reflected "a clear defense-oriented shift" in Japan's budgets. Officials pointed out that the agency's request for a 24.9 percent increase to $186.8 million in support payments for the maintenance of U.S. military facilities was approved in full.