Cuba battled for international recognition as the leader of the nonaligned movement today in a marathon struggle to win a seat on the United Nations Security Council for the next two years.

After a full day of voting -- 13 ballots by members of the U.N. General Assembly -- the outcome remained in doubt, with the rival Colombian delegation maintaining support from a third of the assembly, enough to prevent a Cuban victory.

The United States, fearing that the Cuban presence would make life more difficult for the West and would provide a rhetorical outlet for Cuban anti-americanism, was lobbying to hold the line.

The intitial vote -- 77 for Cuba and 68 for Colombia stunned -- U.S. dipolmats, who had predicted earlier that Colombia would start out with a slim lead, and that the Cuban votes would erode.

In fact, the Cuban lead increased. It reached a high of 84 votes -- shy of the 96 needed for a two-thirds majority -- on the seventh ballot.

Diplomats participating in the consultations finaly agreed that the assembly should adjourn until Tuesday so that negotiations could take place on a compromise.

This could result in a sharing of the two-year term on the Security Council, which as happened before, or in the choice of a compromise candidate from Latin America.

For Cuba, the acquiescence to a third candidate would be considered a defeat for Havana's aspirations to an international post from which it could be seen leading the nonaligned movement.

Under normal circumstances, a candidate from the 92-nation group would sweep any U.N. office for which it chose to run. But the Cubans alienated a number of Third World nations by their domineering tactics at last month's nonaligned conference in Havana. And there was stiff resistance among Latin Americans, Western nations and the Chinese.

The other four Security Council seats up for election today were taken by Tunisia, Niger, East Germany and the Philippines, none of which faced formal opposition. These countries will replace Kuwait, Gabon, Czechoslovakia and Nigeria, whose two-year terms on the 15-nation council expire Dec. 31.

Colombia and Cuba were contending for the seat being vacated by Bolivia.

The other five nonpermanent members of the council, whose terms run through the end of 1980, are Bangladesh, Jamaica, Norway, Portugal and Zambia.