Earl now has speeds of up to 80mph, with the eye of the storm now passing just north of Belize City.
Belize’s National Emergency Management Organization (NEMO) warned of flash flooding and mudslides in Earl’s wake.
Heavy rains have fallen on Honduras. The storm is forecast to continue through northern Guatemala into Mexico.
Authorities have urged Belize City residents and other coastal communities to move inland and take advantage of higher ground or a network of storm shelters.
Officials ordered the closure of Belize City’s international airport while archaeological reserves and national parks were also shut.
The storm is expected to lessen when as it moves inland.
In the meantime, NEMO officials say heavy rain could cause flash floods and mudslides, with a storm surge possible along the shore.
They have warned of trees being blown down, power cuts and damage to houses and buildings which will be hit by flying objects and projectiles.
After Earl passes through across Belize, it is expected to go through a northern rural part of Guatemala and from there into south-eastern Mexico.
Guatemala at this time of the year has its rainy season with often fatal flooding and mudslides.
Meanwhile, Mexican authorities say that the southern states of Campeche, Quintana Roo, Tabasco and Yucatan are likely to be affected by Earl and have issued an alert.
The storm knocked over a large numbers of trees and utility poles in Honduras, officials say.
At least nine people died on August 1 in Haiti and the Dominican Republic as the storm passed over the Caribbean.
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