"The tsunami threat from this earthquake has passed and there is no further threat", announces the American Pacific Tsunami Warning Center.
Earlier, warnings had been issued that affected about a dozen countries and waves of up to three meters were at risk of hitting Cuba's coast, where residents were urged to move inland.
Waves of up to one meter were also feared to cause damage on the Cayman Islands.
"This was a major earthquake and we are grateful that no major damage has been reported on our islands", the authorities there wrote in connection with the all-clear being given.
The earthquake with a magnitude of 7.6 occurred in the sea about 209 kilometers southwest of the Cayman Islands, according to the US Geological Survey.
