Premier Adolfo Suarez announced tonight that he would run for Parliament in next month's national elections.

Overcoming their disunity, his centrist backers formed a coalition pledged to support Suarez and his policies.

The two moves virtually assure that the premier will be returned to office, this time with an electoral mandate to carry out the reform program that he and King Juan Carlos have been trying to implement over the objections of the rightist remnants of the dictatorship of the late Generalisimo Francisco Franco.

The king appointed Suarez, 44, premier last year to carry out the reform program, which is to culminate next month in parliamentary elections.

Speaking on nationwide television, Suarez clearly identified himself with the center. He stressed that most Spaniards are moderates who, like himself, want to avoid dividing the country again into two warring camps.

This was a clear allusion to the Civil War and to the dictatorship of Franco, who stifled political life from the end of the conflict in 1939 until his death nearly 18 months ago.

In his talk, Suarez carefully avoided mentioning that the right, which has attacked Suarez' decision to legalize the Communist Party and invoked Franco repeatedly, will be his principal opponent in Spain's first free election in 41 years.

The premier forcefully defended his decision to legalize the Communist Party, explaining that the step was necessary before the election because the country must know the party's real strength.

The premier's decision was carefully orchestrated. He waited until returning from Washington, where President Carter praised King Juan Carlos and Suarez for their efforts to bring democracy to Spain, reinforcing Suarez' image as a dedicated moderate.

A careful politician who is guided by government and private public opinion polls. Suarez delayed announcing his final plans until the disarrayed political parties of Spain's center finally formed an electoral coalition pledged to support him and his policies.

The pro-Suarez grouping of 15 center-right and center-left political parties, ranging from Christian Democrats to Liberals, was forged by Leopoldo Calvo Sotelo, who resigned as public works minister only last Saturday. A close political collaborator of Suarez, he enjoys the king's confidence.

The new party, called the Democratic Center Union, was formally registered today, hours before a midnight deadline.

The union appears to have a broad base that could attract Spanish voters who are confused by the large number of parties seeking to participate in the election. In the past few weeks, 151 national and regional parties have been legalized.

With Suarez as a candidate for the coalition, moderates could emerge as a political force to deal with pressing demands for constitutional change, tax laws and regional freedom. Left-wing Christian Democrats refused to join the coalition, however.

As the architect of electoral reforms and as the politician who took the risk of legalizing the Communist Party, Suarez has won the sympathy of leftists and the hostility of rightists.

His main opposition comes from the well-heeled rightist Popular Alliance Party, dedicated to preserving much of Franco's heritage. Popular Alliance candidates have been stumping the country playing on the fear of communism that Franco exploited during and after the Civil War. Suarez is being portrayed as a traitor for ending Franco's ban on the Communists.

The strength shown by the rightists apparently sparked center parties into getting behind the premier.

Under the new electoral law, the premier is the only Cabinet minister who can run for election next month. The rightists have attacked this provision and a spokesman for the alliance said it is considering challenging Suarez right to be a candidate.