(CNN) The east coast of Mexico's Yucatan Peninsula is under a hurricane warning as Tropical Storm Grace makes its way across the Caribbean, the National Hurricane Center said.
The storm was about 50 miles west of Montego Bay, Jamaica, on Tuesday evening, with maximum sustained winds of 60 mph. It was moving west at 15 mph.
The Cayman Islands are under a hurricane watch, the NHC said.
"Grace is forecast to strengthen into a hurricane on Wednesday, with some additional strengthening possible prior to the center reaching the Yucatan Peninsula," the NHC said.
The hurricane warning extends from Cancun to Punta Herrero and includes Cozumel, the NHC said.
Grace brought heavy rain Tuesday afternoon to earthquake-shattered Haiti, Jamaica and eastern Cuba.
The center of Grace will move over Jamaica with tropical storm-force winds, strong surf and flooding rains, the National Hurricane Center said.
Tropical storm warnings were in effect for Jamaica, the Cayman islands and several provinces in Cuba, the NHC said.
Overnight, Grace's center passed briefly over Haiti's Tiburon Peninsula, bringing heavy rains, the NHC said.
Grace was expected to produce another few inches of rain to the area recovering from a 7.2-magnitude earthquake that hit Saturday, killing at least 1,419 people.
The NHC said the rainfall could lead to flash and urban flooding and possible mudslides.
Over the next several days, Grace is expected to continue west to west northwest, moving near the Cayman Islands on Tuesday night and approaching the Yucatan peninsula of Mexico late Wednesday or early Thursday, the NHC said.
The Cayman Islands may see hurricane conditions early Wednesday, according to the NHC, and tropical storm conditions could begin as early as Wednesday evening in the Yucatan Peninsula.
The area will likely get 3 to 6 inches of rain, which may lead to flash flooding and urban flooding.