By David Alire Garcia

ACAPULCO, Mexico (Reuters) - More heavy rain spawned by Hurricane Raymond as it churns over the Pacific fell on southwestern Mexico on Tuesday, soaking areas hit by record flooding last month, but forecasters said the storm was weakening and appeared unlikely to reach land.

The port and schools remained closed in the resort city of Acapulco, which also was battered by tropical storms that struck Mexico in mid-September. The freight hub of Lazaro Cardenas to the northwest also was shut.

Coastal rains caused minor mudslides in the hills behind Acapulco, but there were no reports of significant damage.

The U.S. National Hurricane Center downgraded Raymond one notch to category 2 in the five-step hurricane intensity scale.

Raymond, located about 85 miles off the coast of Guerrero state and 135 miles west-southwest of Acapulco, generated winds of up to 105 miles per hour and may draw nearer to land before starting to move slowly out to sea on Wednesday, the Miami-based center said.

The hurricane was stationary on Tuesday, the forecasters said.

Heavy rain came down overnight in Acapulco, but by Tuesday morning only a slight drizzle was falling with light winds. People moved about freely, beaches were open and there were no signs of serious flooding in the city center.

The city nearest to the threat of Raymond is Zihuatanejo to the northwest of Acapulco.

Mexico has no major oil installations in the area at risk from Raymond, which has prompted hurricane alerts from Acapulco in Guerrero up to Lazaro Cardenas in the state of Michoacan.

The hurricane is expected to produce between four and eight inches of rain in Guerrero and Michoacan, and in isolated cases as much as 12 inches, forecasters said.

Mexico last month suffered its worst flooding since records began when storms Manuel and Ingrid converged from the Pacific and the Gulf of Mexico, killing more than 150 people and causing damage estimated at around $6 billion.

About 5,700 people are still living in shelters in Acapulco due to the impact of the storms, according to the local government.

Torrential rains brought hotel occupancy rates in the beach resort to record lows last month and flooded Acapulco's airport, stranding thousands of tourists. The city's airport was operating normally on Tuesday, authorities said.

(Writing by Dave Graham; Editing by Simon Gardner and Will Dunham)