Gov. Josh Green of Hawaii declared an emergency on Tuesday ahead of a tsunami that was expected to reach the state within hours, after a rare 8.8-magnitude earthquake struck off Russia’s eastern coast.

Sirens and cellphone alerts blared across Hawaii’s islands on Tuesday afternoon. The first wave was expected to arrive at 7:10 p.m. local time, the state’s emergency authorities said.

Mr. Green said on social media that emergency operations centers had been fully activated, and he urged residents to take the situation seriously.

“If you are in a coastal area, move inland and to higher ground immediately. Do not wait,” he said.

On Hawaii’s Big Island, a cruise ship docked in Kailua-Kona harbor summoned its passengers back to the boat with a siren. Police officers warned tourists at food trucks to leave.

Many people on Oahu, where Honolulu is situated, did not wait for official advice to seek higher ground, and traffic was dense along mountain roads.

Among the early evacuees was Jaqueline Mylroie, who owns a general store in Puakō, a coastal community on the Big Island, and was trying to find shelter in Waimea, which is on higher ground. Some of her neighbors in Puakō had not left yet, Ms. Mylroie said.

The earthquake, about 78 miles east-southeast of Petropavlovsk-Kamchatsky, Russia, took place at 7:24 p.m. Tuesday Eastern time, according to the U.S. Geological Survey. It could be the sixth-strongest earthquake ever recorded, according to the Geological Survey, whose seismologists often revise the magnitude of earthquakes as they gather more data.

Tsunami warnings were also issued for Japan’s Pacific coast and two eastern regions of Russia, and watches and advisories were in effect along the West Coast of the United States and as far away as Chile. The National Weather Service warned people in California to stay away from beaches and waterways.