The Interior Ministry said 22 people died in Guerrero, Hidalgo, Oaxaca and Puebla states, and 12 people were killed in landslide in Veracruz, El Universal reported
Interior Minister Miguel Angel Osorio said he was instructed by Mexican President Enrique Pena Nieto to work jointly with federal agencies to help provide humanitarian aid and safety in the most affected areas.
Tropical Storm Manuel battered Mexico's western coast while Hurricane Ingrid brought heavy rains to the country's gulf coast before the Category 1 hurricane was downgraded to a tropical storm.
Officials said rain likely will linger for several days, which could cause flooding and mudslides, El Universal said.
Officials said the airport in Acapulco remained closed because of electrical infrastructure damage.
Roads and bridges were closed because of flooding and landslides.
El Universal said the federal government issued an emergency declaration to assist 49 municipalities affected by storms.