Agatha was centered about 170 miles (275 kilometers) southwest of Puerto de San Jose, Guatemala, and moving toward the northeast at 5 mph (8 kph), said the U.S. National Hurricane Center in Miami. It had maximum sustained winds of 40 mph (64 kph) and some strengthening was expected.
The storm was expected to dump from 10 to 20 inches (25 to 50 centimeters) of rain and as much as 30 inches (75 centimeters) in isolated areas of Guatemala, threatening dangerous floods and mudslides.
A tropical storm warning was in effect Sunday for a stretch of coastline from El Salvador to far-southern Mexico.
Guatemalan disaster relief spokesman David Leon said officials worry that the rains could exacerbate damage in the country, where explosions from the Pacaya volcano have destroyed 800 homes this week.
Leon said two children and two adults were killed Saturday when rains generated by Agatha dislodged a boulder that crushed a house they were in. The deaths happened in the department of Quetzaltenango, 125 miles (200 kilometers) west of Guatemala City and outside the area affected by Pacaya.
Pacaya, which is just south of the capital, started spewing lava and rocks Thursday afternoon, blanketing the capital with ash and forcing the closure of the international airport. A TV reporter was killed by a shower of burning rocks when he got too close.
Airport official Felipe Castaneda told reporters Saturday that the airport would be closed for the next five days.
"The work to remove the ash was going forward, but the rain has complicated it," Castaneda said.
In El Salvador, authorities began evacuating hundreds of families in areas at risk for landslides and flooding, suspending fishing and tourism along the Pacific coast.
Five days of steady rainfall has already swollen a major river flowing through the capital San Salvador.
Meanwhile in Ecuador, strong explosions that rocked the Tungurahua volcano and prompted evacuations of 2,500 people eased Saturday.
"The danger lever of the volcano has been reduced," said Geophysical Institute monitor Mario Ruiz. The number of explosions had tapered off and there were no lava flows, he added.
Tungurahua, 95 miles (150 kilometers) southeast of the Ecuadorean capital of Quito, buried entire villages in 2006, killing at least four and leaving thousands homeless.