At least three people have been confirmed dead and at least five others were reported missing after record-breaking storm Agatha battered southern Mexico, local authorities have said.

Aldis Lopez, 21, and Mario Cruz, 18, were the storm's first confirmed victims in the community of Santa Catarina Xanaguia in the hardest hit state of Oaxaca.

"They were buried between rocks and mud," Axel Martinez, a spokesperson for the Oaxaca's civil protection agency, told Reuters.

The civil protection agency confirmed a third person had died in the town of San Mateo Pinas, a woman who got caught in a landslide.

Five others were reported missing, according to the state's public security secretary.

A view of the sea before Hurricane Agatha makes landfall in Huatulco, Oaxaca State

Agatha made landfall as a Category 2 hurricane yesterday afternoon, touching down with 169 kilometre-per-hour winds near the beach town of Puerto Angel on the Pacific coast, losing strength as it moved inland.

By early today, it had weakened to a tropical depression with winds of 45 kilometres-per-hour and was expected to dissipate by afternoon, according to the US National Hurricane Center (NHC), which warned of life-threatening flash floods and mudslides in Oaxaca state.

In a news conference, Mexican President Andres Manuel Lopez Obrador said he would meet with authorities and security advisors to monitor the situation.

Waves of between one and three meters were expected to hit the coasts of Oaxaca and Chiapas during the day, Mexico's National Water Commission CONAGUA said on Twitter.

Municipal police officers patrol as rain falls during the arrival of Hurricane Agatha

Rain caused mud and rocks to slide onto two highways in Oaxaca, blocking access to at least one area of the state, local authorities said. Mexico's transportation ministry was working to clear the roads into the night on Monday.

Some towns in Oaxaca lost power and one transformer exploded, officials said. Telephone lines were knocked out yesterday, forcing authorities to communicate by radio.

Agatha, the strongest hurricane on record to reach land on Mexico's Pacific coast during the month of May, is expected to drop a total of 10 to 16 inches of rain on Oaxaca, with heavy downpours in nearby states of Chiapas, Veracruz, Tabasco and eastern Guerrero, the NHC said.