A new parallel programming framework for DNA sequence alignment in homogeneous multi-core processor architectures is proposed. Contrasting with traditional coarse-grained parallel approaches, that divide the considered database in several smaller subsets of complete sequences to be aligned with the query sequence, the presented methodology is based on a slicing procedure of both the query and the database sequence under consideration in several tiles/chunks that are concurrently processed by the several cores available in the multi-core processor. The obtained experimental results have proven that significant accelerations of traditional biological sequence alignment algorithms can be obtained, reaching a speedup that is linear with the number of available processing cores and very close to the theoretical maximum.