Prime Minister Masayoshi Ohira, teetering on the brink of a forced resignation, failed today to reach agreement with the archrival who is trying to push him out.

The embattled prime minister met for three hours with former prime minister Takeo Fukuda, who said later that no conclusions had been reached.

Fukuda is leading a Liberal Democratic Party campaign to force Ohira to resign as a way of taking responsibility for their party's poor showing in elections two weeks age. Ohira has refused and tonight said after the meeting that he has not changed his mind.

The two-week impasse has created an intense intraparty battle, has revived longstanding personal feuds, and has threatened a leadership vacuum that could stall the government.

Various compromises have been suggested, including one that would leave Ohira in office but force him to turn over much of his party power to political enemies.

Fukuda today apparently gave the prime minister a stern lecture on what he should do to accept responsibility for the party's election setback. Even Ohira characterized the message as "severe."

But Ohira said he merely agreed to "deeply consider" Fukuda's works and to meet again "if the circumstances require."

The unusually bitter factional struggle began almost as soon as the polls closed Oct. 7. Two major factional leaders, Fukuda and former prime minister Takeo Miki, bluntly demanded that Ohira abandon office, and a third, Yasuhiro Nakasone, pointedly called for a new leadership arrangement to resolve the dispute.

There have been charges of bad faith and misrepresentation from the anti-Ohira factions, and it appeared on several occasions that the prime minister would be forced out by the pressure.

But he has held on stubbornly through a series of painful meetings with Fukuda and other party leaders.

Adding to the pressure have been unusually blunt editorials in leading Japanese newspapers. The Ashahi newspapers, in an editorial entitled "Ohira Should Go," suggested that Ohira's only concern has become one of "holding onto power on the basis of the strength of his faction." That was a disgrace," the editorial declared.

The pressure from within his party stems from a widespread conviction that he committed political errors in staging the lower house elections this fall and should resign as a consequence.

It is a practice in many Japanese instituations to resign as a way of taking responsibility for misjudgements. Miki resigned after the 1976 election, even though his party had done slightly better then than Ohira's did in early October.

One fidderence is that Miki then had little support from any faction but his own. Ohira enjoys the favor of the large faction led by former prime minister Kakuei Tanaka, and together they command support from 95 Liberal Democratic Party members, about 40 percent of the total in Parliment.

Against the wishes of many party members, Ohira had pushed through his decision to dissolve the lower house and call for new elections. He said it was necessary to achieve a "stable majority" to pass key legislation and set his sights on winning 271 seats. Instead, the Liberal Democrats won 248 seats, a net loss of one seat.

His second blunder, party associates say, was in focusing attention on a new consumer tax he proposed to levy next year. It proved to be vastly unpopular with the voters, particularly with small businessmen. About 70 percent of his own party's candidates came out against the tax, and Ohira finally had to disavow it.

On party member described the Ohira tax plan today as a "terrible mistake."

He agreed that a tax increase will be necessary to reduce Japan's budget deficits, but he said Ohira had failed to explain his version properly and in the end put most of his party's candidates on the defensive.

"His theory was right but his technique was wrong," the party members, Bunsei Sato, said.

In the past when the Liberal Democratic Party factional struggles have gotten out of hand, leading party elders whose prestige was high have stepped in to settle matters in a quiet, gentlemenly fashion. This time the only elder available was Eiichi Nishimura, who is closely identified with Tanka, Ohira's ally, and his intervention has produced no results so far.

Conducting a kind of shuttle diplomacy among the factional leaders, Nishimura emerged from one meeting with Ohira with what seemed to be a comfortable solution. He said Ohira had agreed to leave everything in his hands -- including the crucial decision on whether or not Ohira should resign. It was a first taken as a binding commitment to bow out if Nishimura said he should.

But then Ohira said he had not meant that at all and insisted on making his own decision on whether to resign. Fukuda cried foul and refused for one day to meet with Ohira.