Tropical Storm Ingrid and the remnants of Tropical Storm Manuel drenched Mexico's Pacific and Gulf coasts with torrential rains Monday, flooding towns and cities, cutting off highways and setting off deadly landslides in a national emergency that federal authorities said had caused at least 33 deaths.

The governor of the Gulf Coast state of Veracruz announced Monday afternoon that 12 people had been killed when a landslide hit a bus travelling through the town of Altotonga, about 60 kilometres northwest of the state capital. Gov. Javier Duarte said the death toll could grow as bodies were recovered.

More than 23,000 people have fled their homes in the state due to heavy rains and 9,000 are in emergency shelters.

The heaviest blow Sunday fell on the southern coastal state of Guerrero, where Mexico's government reported 14 confirmed deaths. State officials said people had been killed in landslides, drownings in a swollen river and a truck crash on a rain-slickened mountain highway.

Mexico's federal Civil Protection coordinator, Luis Felipe Puente, told reporters late Sunday that stormy weather from one or both of the two systems also caused three deaths in Hidalgo, three in Puebla and one in Oaxaca.

Getting hit by a tropical storm and a hurricane at the same time "is completely atypical" for Mexico, Juan Manuel Caballero, coordinator of the country's National Weather Service, said at a news conference with Puente.

Authorities in the Gulf states of Tamaulipas and Veracruz evacuated more than 7,000 people from low-lying areas as the hurricane closed in, and the prospect of severe weather prompted some communities to cancel Independence Day celebrations planned for Sunday and Monday.

Both storms are a risk to cause landslides. (CBC)

Manuel came ashore as a tropical storm Sunday afternoon near the Pacific port of Manzanillo, but quickly began losing strength and was downgraded to a tropical depression late Sunday, although officials warned its rains could still cause flash floods and mudslides. The U.S. National Hurricane Center said the system dissipated early Monday.

The rains caused some rivers to overflow in Guerrero, damaging hundreds of homes and disrupting communications for several hours.

Early Monday, Manuel's remnants had maximum sustained winds of about 45 km/h and was moving to the northwest at 13 km/h. It was about 10 kilometres west of Puerto Vallarta.

Manuel was expected to dump up to 40 centimetres of rain over parts of Guerrero and Michoacan states, with maximums of 60 centimetres possible in some isolated areas. Authorities said the rains presented a dangerous threat in mountains, where flash floods and mudslides were possible.

Ingrid also was expected to bring very heavy rains. It had maximum sustained winds of 95 km/h early Monday and was centred about 40 kilometres west of the coastal town of La Pesca in the border state of Tamaulipas. It was moving west-northwest at 13 km/h. A tropical storm warning was in effect from La Cruz to Rio San Fernando.

More than 1,000 homes in Veracruz state had been affected by the storm to varying degrees, and 20 highways and 12 bridges were damaged, the state's civil protection authority said. A bridge collapsed near the northern Veracruz city of Misantla on Friday, cutting off the area from the state capital, Xalapa.