MEXICO CITY—Five years after Mexican President Felipe Calderón declared war on the country's violent drug traffickers, his government is fighting accusations by human-rights activists that it allowed the killing, torture and kidnapping of civilians in its drug war.

While the government denies systematic abuses, mounting reports of such cases could erode popular support for the offensive by Mr. Calderón. And with Mr. Calderón's legacy largely built on his fight against organized crime, the reports could also hurt his party's...