Police in the Tongan capital, Nuku'alofa, said there were no immediate reports of injury or damage.
Local resident Pesi Fonua said the quake "lasted for something like 20 seconds," but "I haven't seen any damage from it."
The Hawaii-based Pacific Tsunami Warning Center issued a tsunami warning for Tonga and neighboring islands, and reported that sea level readings have confirmed that a potentially destructive tsunami wave was generated by the quake.
Local radio stations in Tonga broadcast warnings that a tsunami was possible and that people should move away from coastal villages, but police and locals said no big wave had been reported. Police spokesman Niua Kama said residents did not appear to take the warning seriously.
"People are out on the roads, laughing at the warning," he told The Associated Press. "They are not moving from the coast" even though there had been "a strong warning of a tsunami. Police have not taken any action at this stage."
The tsunami center also advised that some coastal areas of Hawaii could see a rise in sea level and strong currents lasting up to several hours.
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