The ships will be safer out at sea than if they were tied to piers where they could be banged around by the waves, the Navy said.
A tsunami wave can travel at up to 600 mph, said Jenifer Rhoades, tsunami program manager at the National Weather Service.
Some Pacific nations in the warning area were heavily damaged by a tsunami last year.
The Sept. 29 tsunami, created by a magnitude-8.3 earthquake, killed 34 people in American Samoa along with the deaths in Samoa and Tonga. Scientists later said that wave was 46 feet (14 meters) high.
The tsunami warning center said the waves reached the islands so quickly residents had only about 10 minutes to respond to its alert.
During the devastating December 2004 Indian Ocean tsunami, there was little to no warning and much confusion about the impending waves. The tsunami eradicated entire coastal communities the morning after Christmas, killing 230,000 people.
In Hilo, officials cordoned off the first three blocks next to the beach. A few people watched the still ocean as a whale swam off the coast, but streets were mostly empty as tsunami sirens blared. Gas stations had long lines, some 10 cars deep.
Hawaii Gov. Linda Lingle declared a state of emergency. She said leprosy patients from the Kalaupapa settlement on Molokai have been moved to higher ground before the waves arrived.
Past South American earthquakes have had deadly effects across the Pacific.
A tsunami after a magnitude-9.5 quake that struck Chile in 1960, the largest earthquake ever recorded, killed about 140 people in Japan, 61 in Hawaii and 32 in the Philippines. It was about 3.3 to 13 feet (one to four meters) in height, Japan's Meteorological Agency said.
Japanese public broadcaster NHK quoted earthquake experts as saying the tsunami would likely be tens of centimeters (inches) high when it reaches the country. A tsunami of 28 centimeters (11 inches) was recorded after a magnitude-8.4 earthquake near Chile in 2001.
Seismologist Fumihiko Imamura, of Japan's Tohoku University, told NHK that residents near ocean shores should not underestimate the power of a tsunami even though they may be generated by quakes on the other side of the ocean.
"There is the possibility that it could reach Japan without losing its strength," he said.
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