At least 13 people have been killed by a tornado that hit the northern Mexico border city of Ciudad Acuna.
Hundreds of homes have been damaged or destroyed in the city, in Coahuila state, just across the border from Del Rio, Texas.
Many other people have been injured and there are fears the death toll could rise in the coming hours.
There has also been severe flooding across the southern US, with at least eight dead and 12 missing.
Images from Mexico showed cars and buildings badly damaged.
Coahuila Governor Ruben Moreira, on a visit to the stricken area, said 10 adults and three children had died and a baby was missing. Another 150 people had been taken to hospital, he said.
The authorities say that more than 1,000 homes have been damaged by the storm.
At one point the tornado reached a speed of 270-300km/h (168-186mph). Most of those who died were walking on the street when it struck, officials said.
The missing baby's child carrier was ripped from its mother's hands by a sudden gust of wind, Coahuila state Interior Secretary Victor Zamora told the AP news agency.
Ciudad Acuna Mayor Evaristo Lenin Perez said that it was the first tornado to hit Acuna since the city's foundation, more than 100 years ago.
Rescuers were searching the 750 damaged properties for more casualties.
"There are cars on top of houses, there are dead people lying in the street, it is total chaos," said local resident Maria del Rosario Ramirez, quoted by Mexican newspaper La Jornada.
The BBC's Katy Watson in Mexico
The tornado only lasted a short moment but that was enough to devastate a community. It struck at a busy time in the morning - people were driving or taking public transport to work. Cars were catapulted towards buildings, roofs ripped off and many vehicles left upended.
Residents of Ciudad Acuna are used to hearing about this sort of thing north of the border in Texas, not experiencing this first-hand. The infrastructure clearly wasn't strong enough to stand up to the impact - the army is helping to search for missing people and neighbouring states have also said they will lend a hand in the rescue effort.
Mexican President Enrique Pena Nieto expressed his "solidarity" with the relatives of the victims, and later travelled to some of the areas affected by the storm.
He said the government would "take stock of the damage and provide all appropriate support".
Victor Zamora, Coahuila's interior secretary, said an area of about seven blocks had been "devastated" by the tornado, which struck at about 06:10 (11:10 GMT).
Civil protection officials said that eight temporary shelters had been set up for those made homeless by the disaster.
In the southern US, warnings and alerts stretched from Colorado through to Arkansas, Louisiana, Missouri and eastern Kansas.
Twelve people were missing after flash floods struck the Blanco river in central Texas on Sunday, including Laura McComb and her two young children.
Her sister Julie Shields said Mrs McComb called her to say her holiday home had been washed away and she was "floating down the river".
"She said: 'Call mom and dad. I love you, and pray'," Ms Shields She told local television channel KXAN.
The storms have been blamed for four deaths in Texas so far, including a 14-year-old who was found along with his dog in a storm drain.
The Oklahoma Department of Emergency Management also reported four fatalities between Saturday and Monday across the state, which also saw severe flooding and reported tornadoes.
Texas governor Greg Abbott said it was the worst flooding the state had seen, and that the wave of water had a "tsunami-like" power.
He has declared a state of disaster in 24 counties.
In the city of San Marcos, residents were forced to evacuate their homes as the flood waters rose after torrential rain that turned streets into fast-flowing rivers.
The floods damaged hundreds of homes, some of them swept off their foundations.
A tornado also damaged a block of flats in Houston over the weekend.