MEXICO CITY — The Mexican drug war that has largely been defined by violence along the border is intensifying in interior and southern areas once thought clear of the carnage, broadening a conflict that has already overwhelmed the authorities and dispirited the public, according to analysts and new government data.

Last week, two headless bodies were found in a smoldering minivan near the entrance to one of the largest and most expensive malls in Mexico City, generally considered a refuge from the grisly atrocities that have gripped other cities throughout the drug war.

Two other cities considered safe just six months ago — Guadalajara and Veracruz — have experienced their own episodes of brutality: 26 bodies were left in the heart of Guadalajara late last year, on the eve of Latin America’s most prestigious book fair, and last month the entire police force in Veracruz was dismissed after state officials determined that it was too corrupt to patrol a city where 35 bodies were dumped on a road in September.

The spreading violence, believed to largely reflect a widening turf war between two of the biggest criminal organizations in the country, has implications on both sides of the border, putting added pressure on political and law enforcement leaders who are already struggling to show that their strategies are working.