Authorities worked overnight into Tuesday to clear highways blocked by mudslides along Mexico's southern coast as Tropical Storm Agatha barrelled down on the country, bringing torrential rains and strong winds.

Agatha made landfall as a Category 2 hurricane on Monday afternoon, touching down with 105 miles per hour winds (169 kilometres per hour) near the beach town of Puerto Angel on the Pacific coast.

By Monday evening Agatha weakened to a tropical storm and is expected to dissipate further by Tuesday evening, according to the U.S. National Hurricane Center (NHC), which maintained a warning of life-threatening flash floods and mudslides in Oaxaca state.

Rain caused mud and rocks to slide into 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 late on Monday evening.

Some towns in Oaxaca were left without electricity, and one transformer exploded, authorities said. Telephone lines were knocked out on Monday, forcing authorities to communicate by radio.

Agatha is expected to drop a total of 10 to 16 inches (25-41 centimetres) of rain on Oaxaca, with heavy downpours in nearby states of Chiapas, Veracruz, Tabasco and eastern Guerrero, the NHC said.