A hurricane warning was in effect for Belize and western Honduras, where Richard dumped heavy rains on the coast and the Bay Islands, which are popular with tourists and divers.
The storm's winds strengthened to 85 mph (140 kph), and its center was located about 95 miles (155 kilometers) east-southeast of Belize City, according to the U.S. National Hurricane Center in Miami.
Richard was moving west-northwest at about 12 mph (19 kph) on a projected path that would take it right at Belize City, according to the center. Forecasters said Richard could strengthen to a Category 2 hurricane before hitting land.
Belize City is full of wooden, tin-roofed houses that are highly vulnerable to strong winds. It was devastated by Hurricane Hattie in 1961, prompting officials to move the capital inland to Belmopan. But Belize City is still the nation's largest population center, with about 100,000 inhabitants - a third of the country's population.
However officials in Belize said they expected Richard to hit somewhat south of the capital, between Belize City and the coastal town of Dangriga. They warned people living in flimsy homes or low-lying areas to evacuate, and shelters at schools and other public buildings began filling up.
The National Emergency Management Organization also urged merchants not to raise prices for people who rushed to stores to stock up on basic necessities as the hurricane approached.
On Roatan, in Honduras's Bay Islands, observers reported winds of up to 58 mph (93 kph). More than 90 people took refuge in shelters in the Bay Islands, which lie between Honduras and Belize.
Lisandro Rosales, the head of Honduras' Permanent Emergency Commission, said no deaths or injuries had been reported in Honduras so far.
But Richard's heavy rains did cause a landslide that blocked a highway in northern Colon province, cutting off about 15,000 residents in 40 small towns. Crews were working to clear the road.
Mexico issued a hurricane watch for its southern Caribbean coast, and while Richard is expected to cross over the Yucatan peninsula and re-emerge in the Gulf of Mexico, forecasters said it is likely to weaken and dissipate over Gulf waters.
Authorities said dangerous floods and mudslides were still possible in Honduras and declared states of maximum alert in four coastal provinces.
The hurricane center said Richard could cause "large, destructive waves" and storm surges of 2 to 4 feet above normal tides in Honduras and Belize. The storm could bring 3 to 5 inches (7 to 13 centimeters) of rain to northern Honduras and as much as 7 inches (18 centimeters) in some spots.
Tropical storm-force winds extended 105 miles (165 kilometers) from the hurricane's center.