WASHINGTON, Sept. 12 (AP)--President Kennedy said today that he did not favor military action against Cuba. Such action was suggested by the American Legion at its convention in Miami.

The President was told that the convention had asked the United States to "proceed boldly alone" to end Communist rule in Cuba if other nations of the hemisphere would not join in such an effort.

At his news conference, the President said the United States had taken every step short of military action against the Communist regime of Premier Fidel Castro.

He added that it is quite obvious that Cuba is a Soviet satellite, and that Premier Castro was serving the Soviet Union.

But military action, the President continued, would not be in the best interests of the United States and could bring grief to the people of Western Europe.

It is believed he meant that United States military action against Cuba could produce serious troubles for the free nations of Europe.

At another point in his news conference, however, the President indicated that there had been no change in his previously announced stand that the United States would take any measures necessary to protect its national security.

MOSCOW, Sept. 12 -- The Soviet Union combined today a warning to the United States over Cuba with an admonition to Premier Fidel Castro to show more restraint and accede to the treaty for a limited nuclear test ban.

It said that the "establishment of normal relations between the United States and Cuba would be in the interest of both states and would promote peace and international security."

The admonitions were contained in an article in Pravda, organ of the Soviet Communist party. It was signed `'Observer," a signature usually reserved for major policy statements reflecting the views of the Soviet leadership.

The Castro Government is one of five Communist regime that have not signed the test ban treaty. Unlike the others, it is dependent on Soviet military and economic assistance.

The other Communist countries that have not acceded to the treaty are China, North Vietnam, North Korea and Albania.

The Article opened by praising the test ban treaty as inspiring "all mankind"' with hope, and added:

"The world public awaits from all governments further steps, normalizing the situation relaxing international tension and strengthening peace."

The article gave a lengthy account of Cuban press reports of air attacks on Cuba.

It implied that the best hopes that Cuba had in the face of such attacks was, on the one hand, the test ban treaty and, on the other hand, Soviet military protection.