TOKYO, OCT. 8 -- Three well-known Japanese politicians officially kicked off their campaigns for the prime ministership today, as the ruling Liberal Democratic Party agreed to hold an election to decide among them in 12 days.

The race to replace Prime Minister Yasuhiro Nakasone has been under way in the backrooms for months, but today the three sexagenarians, known here as "new leaders," officially filed their candidacies. They are former foreign minister Shintaro Abe, 63; Finance Minister Kiichi Miyazawa, 68; and former finance minister Noboru Takeshita, 63.

The three men formally filed for the post of president of the ruling Liberal Democratic Party. Shortly afterward, the party, which has controlled the parliament for 32 years, set Oct. 20 as the date for its legislators to elect one of them to that post. The winner will become prime minister when Nakasone steps down at the end of the month.

On policy matters the three men are nearly identical. All have served in Nakasone's Cabinet and said they expect few changes in policy.

All of them put a close alliance with the United States at the top of their foreign policy goals. They all support tax reform, further measures to open Japanese markets to imports, expansion of the domestic economy and a continuation of Japan's "no war" constitution. All support protecting Japan's politically powerful rice farmers by continuing to restrict imports.

Takeshita leads the party's largest faction, with 114 members of the Diet, or parliament, and therefore is widely viewed as the man to beat. Nakasone has not yet committed the 87-member faction he leads to any candidate.

Takeshita is described as a scrappy political insider who, by his own assessment, is more comfortable working the halls of the Diet than developing broad policy outlines.

Questions about his international judgment surfaced last winter when a Japanese newspaper ran an article in which Takeshita, quoting residents near a big U.S. Navy base here, said that the high yen had forced sailors to stop going out on dates. Instead they were getting drunk with each other and "probably that is the reason they are getting AIDS," he said.

The statement infuriated U.S. Embassy officials. Takeshita this week said he was merely repeating a statement made by a friend, but even so it was "not appropriate" for him to have said it.

Miyazawa heads the next largest faction, of 89 members. A fluent English speaker, he is seen here as particularly strong in international affairs and in formulating policy, but less so in the maneuvers of Japan's politics.

Abe, with an 86-member faction, is described as an adept politician with more international exposure than Takeshita, but he is viewed as a not particularly aggressive leader.

In a style typical of Japan, where harmony and consensus are highly valued, all three have refused to say anything negative about the others. Based on press conferences given this week by the candidates, the campaign is likely to be a pretty tame affair, rhetorically.

"My colleagues are just as good as I am," Miyazawa said at his press conference. "All I can say is I will try my best depending upon my past experience. But my colleagues also have their great merits. . . . Being a Japanese, that's the extent of my modest answer." Today, after officially registering their candidacies, the three held a joint press conference to discuss the race. They agreed to meet this weekend to try to settle the selection among themselves without a vote, which many party members have said could cause bad feelings in the party.