Greek Prime Minister Andreas Papandreou today hailed the outcome of yesterday's nationwide municipal elections as a resounding vote of confidence in his year-old Socialist government.

With the final results in from the first round of the election to pick new mayors and municipal councils, the prime minister claimed victory for his Pan-Hellenic Socialist movement (Pasok) even though the races in the nation's main urban centers proved inconclusive. Many of the governments in these cities, where a large portion of the population is concentrated, will not be determined until runoff elections next Sunday.

Terming the results "a tremendous victory for change," Papandreou said on television early today, "I must admit for my colleagues and myself, for members and cadres of Pasok, this great victory gives us the strength and hope for the great creative work we have undertaken to bring the great change for our country."

"Change" is Pasok's political slogan.

The prime minister's upbeat assessment of the elections, the first public sounding of the Greek electorate since Papandreou was swept into power exactly a year ago, was immediately disputed by political rivals on his right and left.

The conservative New Democracy Party that Papandreou turned out of office and the pro-Moscow Greek Communist Party, which increasingly has tried to appeal to the left wing of his Socialist movement, insisted that the complex electoral results vindicated their criticism of Papandreou and his government.

Assessments of the national beneficiaries of the municipal elections varied greatly, depending on who analyzed the results. It also depended on whether one went back to the results of the last municipal elections in 1978 or the less comparable parliamentary elections last year.

The government based its own assessment on the 1978 election, perhaps the more honest barometer given the historic difference in local and national voting patterns.

On this basis, government spokesman Dimitris Maroudas said today that Pasok-supported candidates had triumphed with indisputable majorities in 84 municipalities. Candidates supported by the New Democracy Party won in 29 localities, while the Communist Party took seven. Maroudas said that in 140 other municipalities no slate won 50 percent of the vote, mandating the runoff elections between the top two candidates.

Pasok officials were confident of victory in these runoffs, where they expected the Communists to vote for Pasok candidates when the final round is between the Socialists and the conservatives.

Explaining why Papandreou had called the election a "crushing defeat for the right," Maroudas pointed out that in 1978 the New Democratic Party had emerged from both rounds of the election with 118 mayoralties to Pasok's 73. Maroudas, projecting beyond next Sunday, said he expected Pasok would end up this time with 172 or 173. Since local governments are expected to play a key role in Papandreou's plans to decentralize Greece's administration, this was likely to gladden Papandreou.

New Democracy Party leader Evan Ghelos Averoff and Communist Party Secretary General Harilaos Florakis, however, chose to use last year's elections to show that they had cut into Pasok's support. In 1981, Pasok won 48.8 percent of the national vote to the New Democratic Party's 35.9 percent and the Communists' 10.96 percent.

The Communists -- who have been trying to capitilize on disenchantment on the socialist left because of Papandreou's failure to implement the radical domestic and foreign policy changes he had advocated -- based their claims to serious gains on the contests in Greece's major urban centers: Athens, Salonika, and Pireas. In these cities, where more than one-third of Greece's 9.5 million citizens live, the Communist vote ranged from 18.5 percent in the capital to 23.5 percent in Salonika.

"The facts speak for themselves and reveal the truth," the communist newspaper Rizos said. "The candidates representing real change have secured new, significant victories. The numbers confirm the [Communists'] influence and prestige."

The conservative New Democracy Party also focused on the urban vote and drew satisfaction from results in Salonika where its candidate for mayor outpolled the Pasok candidate 40.8 percent to 34.1 and in Athens where it was running only slightly behind Pasok mayoral incumbent Dimitrios Beys' 38.3 percent in a five-way race.

Avaroff noted that in Pireas a far right-winger Aristidis Skylitsis, who had been the appointed mayor under the 1967-1974 Greek military government, received 42.14 percent to Pasok's 36.6.

Although the combined Pasok and Communist vote expected in these urban centers next Sunday could well wipe out the New Democracy candidates for mayor, Avaroff said the fact that his candidates had polled more in those cities than the party had in the 1981 national elections was proof of a rightist resurgence.

Since it has been normal for the governing party to do badly in municipal elections and since Pasok made great strides in the once-conservative countryside while largely holding its own in the important cities, Papandreou appeared to have more reason than any of his opponents to feel that the election outcome vindicated his Socialist government in its first year of power.

Papandreou stressed the importance this will mean to his plans for decentralizing the nation's administration and government: "We feel that our people have elected the mayors and community chiefs, the municipal and community councils, with which we can work in building the Greece of tomorrow."