A large 5.8 magnitude quake and two smaller tremors that struck near the capital of Guatemala on Monday have claimed at least three lives in the nearby city of Cuilapa, rescuers said.

"For the moment, we have three dead and various others who have been buried" in rubble, said William de Leon, a spokesman for the volunteer firefighters.

Authorities said mudslides were reported in some areas after hillsides saturated by recent rains gave way.

Landslides cut off access to one of the country's major highways that leads to El Salvador, authorities said.

Seismologists at the United States Geological Survey said the biggest of the three quakes hit at around 12:34pm local time (1834 GMT), and was detected at a depth of 39 kilometres (24 miles), with its epicentre some 52 kilometres (33 miles) southeast of the capital Guatemala City.

It was preceded and then followed by smaller, but still sizable tremors, both measuring 4.8 on the Moment Magnitude Scale.

The quakes were felt as far away as neighbouring El Salvador, where there were no reports of injuries or damage.