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Contiguous strings of length k, called k-mers, are a fundamental element in many bioinformatics tasks. The number of occurrences of a k-mer in a given set of DNA sequencing reads, its k-mer count, has often been used to roughly estimate the copy number of a k-mer in the genome from which the reads were sampled. The problem of estimating copy numbers, called here the k-mer classification problem, has been based on simply analyzing the histogram of counts of all the k-mers in a data set, thus ignoring the positional context and dependency between multiple k-mers that appear nearby in the underlying genome. Here we present an efficient and significantly more accurate method for classifying k-mers by analyzing the sequence of k-mer counts along each sequencing read, called a read profile. By analyzing read profiles, we explicitly incorporate into the model the dependencies between the positionally adjacent k-mers and the sequence context-dependent error rates estimated from the given dataset. For long sequencing reads produced with the accurate high-fidelity (HiFi) sequencing technology, an implementation of our method, ClassPro, outperforms the conventional, histogram-based method in every simulation dataset of fruit fly and human with various realistic values of sequencing coverage and heterozygosity. Within only a few minutes, ClassPro achieves an average accuracy of > 99.99% across reads without repetitive k-mers and > 99.5% across all reads, in a typical fruit fly simulation data set with a 40× coverage. The resulting, more accurate k-mer classifications by ClassPro are in principle expected to improve any k-mer-based downstream analyses for sequenced reads such as read mapping and overlap, spectral alignment and error correction, haplotype phasing, and trio binning to name but a few. ClassPro is available at https://github.com/yoshihikosuzuki/ClassPro.