Those killed included five police officers who were ambushed while patrolling the outskirts of the city early in the morning, The Los Angeles Times reported.
The bodies of eight bullet-riddled men were found in three locations over the next eight hours, police said. Four of them had been beheaded in a way typical of drug traffickers, the Times said. Traffickers have been at war with each other and the government for the last three years.
Guerrero state, which includes Acapulco, is one of Mexico's most violent jurisdictions, the Times reported.
Local news channels have been trying to give a sense of normality to the situation, showing young U.S., Canadian and European tourists already enjoying themselves on Acapulco's beaches, the Times said. A holiday has made a three-day weekend for Mexicans.
But Heriberto Salinas Altes, head of public security in Guerrero said an increase in violence was expected because of new power struggles among drug gangs.
The Times said more than 18,000 have been killed since President Felipe Calderon sent in the army to fight the cartels in December 2006.