Japan has reluctantly begun to grapple again with an issue that has few rivals in terms of its potential to poison trade relations with the United States: whether to extend quotas on exports of automobiles.

The current program, which holds sales to the United States to 2.3 million cars a year, expires March 31. But manufacturers and the government are preparing for closed-door consultations that could continue until then.

They hope to avoid a replay of last spring, when Japan's announcement that it would raise the quota by 24 percent provoked angry cries from Congress and helped push trade relations to their lowest point in years.

Many officials here concede that the timing and tone of that announcement was a public relations fiasco. But they insist that the decision was fundamentally just a step toward free trade.

"We should learn from history and experience," said Makoto Kuroda, head of trade policy at the Ministry of International Trade and Industry. He said no consultations were under way yet and refused to comment further, noting the sensitivity of the issue. "Better to keep quiet," he said.

To date, however, events are unfolding much like they did a year ago. The Japanese appear to be underestimating the emotional wallop the issue carries in Congress, and critics in the United States seem to be assuming that a double-cross is being prepared.

Last week, Japanese newspapers carried brief articles on inside pages quoting an unnamed senior official at the trade ministry as saying that quotas would not be extended, although he said Japan would reconsider in the event of unspecified "big changes" in the general situtation.

The story attracted only minor attention in Tokyo. In many ways it simply reiterated Japan's official position that the quotas are an aberration and must end as soon as possible. The reported reference to "big changes" left adequate leeway for continuing the restraints.

In Congress, however, it drew strong condemnation and seems to have been read as a formal decision for a new "export wave" across the Pacific that would worsen a trade deficit that this year is expected to reach a record $50 billion.

A ministry spokesman denied that any decision had been made. Spokesmen pleaded ignorance about who made the statement. But industry and government sources said privately it was the top man, International Trade Minister Keijiro Murata, talking on background with the reporters who regularly cover him.

Some foreign analysts here called it a trial balloon. But one Japanese official, saying Murata's statement was in response to a reporter's question, called it a case of a politician firing off emotional words without thinking them through.

The quotas began five years ago to give the U.S. automobile industry time to recover from the dark years of the 1970s. Originally a three-year program, the quotas were extended twice for a year each.

The Japanese contend that the quotas' purpose is now accomplished. "The U.S. automobile manufacturers have completely regained their strength, and the unemployed rate is going down," Shoichiro Toyoda, president of the Toyota Motor Corp., said at a press conference yesterday.

Toyoda and others complain that the restraints are in force at a time when the United States is strong-arming Japan to dismantle barriers to imports in its own market. Quotas are a fundamental blemish on the principle of free trade, they say.

Last year, Japanese officials depicted it as a concession when they raised the quota from 1.85 million units to 2.3 million. They could have eliminated it altogether, they said.

As of Oct. 31, seven months into the current program, Japanese companies had shipped 1,471,000 cars to the United States and are expected to reach the full 2.3 million. The United States remains their most profitable market, helping them weather intense competition at home that has wiped out most earnings there.

Japanese companies already have opened a campaign for more access. Following the trade ministry official's words last week, many issued calls for an end to quotas. "Trade imbalance should be solved by looking forward, by stimulating domestic demand in Japan and opening its market," said a spokesman for the Nissan Motor Co., the country's second-largest producer.

At the same time, however, auto executives continue to talk of a need for "orderly marketing," a catch-all phrase meaning the avoidance of torrential exports by less formal means, perhaps self-restraint by individual companies.

Japan has several choices. One would be to retain a quota, as a gesture to Congress, but to raise the numbers again. Or, the quota might be allowed to expire, with Japan switching to behind-the-scenes "administrative guidance." Totally free trade in autos is not commonly considered possible.

At least one analyst, however, predicts that Japan will not only keep the quotas but cut the numbers somewhat. Toshio Obi, an economist who is Japan's representative of Columbia University's East Asia Institute, says Prime Minister Yasuhiro Nakasone cannot risk a blowup two months before he hosts President Reagan and other leaders of the industrialized West at an economic summit meeting here in May.