Prime Minister Yasuhiro Nakasone was forced today into a showdown with his convicted mentor, former prime minister Kakuei Tanaka, and was reported ready to seek Tanaka's resignation from parliament.

Parliamentary business has been stalled for two weeks as opposition parties tried to force Tanaka's resignation and, with no resolution in sight, Nakasone seemed compelled today to make the attempt to nudge him out.

A meeting between the country's two most powerful politicians is considered probable soon.

Tanaka has refused to quit parliament despite his conviction two weeks ago on a bribery charge and there was no indication today that he has changed his mind.

During a day of rumors and widespread speculation, Nakasone did not say that he would seek a resignation and he told reporters only that he would seek Tanaka's "true feelings" on the political troubles.

But reports that leaked out of the ruling Liberal Democratic Party's leadership said that the intent of their meeting is to induce Tanaka to step aside. One party leader said Nakasone would approach him both as a personal friend and as president of the party.

This approach was said to represent an attempt to let Tanaka step gracefully aside for the good of the party and permit the parliament to resume deliberations.

If he accepted that way out, Nakasone would then probably dissolve the lower house and call for early elections. Most observers believe Tanaka would be easily reelected by his still-loyal constituents.

Tanaka was found guilty on Oct. 12 of having accepted a 500 million yen bribe (about $2.1 million) in the Lockheed scandal of the early 1970s and sentenced to four years at hard labor.

Opposition parties immediately pushed for a resolution demanding that Tanaka resign and, when it was bottled up in a Liberal Democratic-controlled committee, refused to attend any sessions.

The government gambled that the opposition would be forced to return to business to vote on two popular bills cutting income taxes and raising wages of public service workers, but the strategy failed and the opposition is still boycotting.

Many observers feel that Tanaka helped solidify the opposition's case with a defiant statement insisting that he is innocent and vowing never to resign so long as appeals are pending.

Japanese custom is for one to resign if his actions cause his institution to be in disgrace. A police lieutenant, for example, would probably resign if a policeman in his jurisdiction committed some embarrassing malfeasance. Many feel that Tanaka has behaved in an un-Japanese fashion by refusing to step aside.

Leading newspapers have demanded that Tanaka quit and public opinion polls show that 80 percent or more of the public think he should get out.

Former prime minister Takeo Miki has insisted that he resign and there are indications that several party members in factions aligned with Tanaka's also want him to leave.

Nakasone is caught in a squeeze because he owes his election last year to Tanaka, who despite his legal troubles still commands the party's largest faction.

He is so powerful, many observers think, that even his resignation from parliament would not diminish his political influence so long as his faction remains loyal and intact. There have been no public defections from his faction since the conviction.

The intense publicity about the case has sparked demands that the Japanese political system be cleansed of the taint of unethical donations of money from big business concerns. Business gives Liberal Democratic candidates large sums of money to finance their campaigns and offices.