The centre issued warnings for Solomon Islands, Vanuatu, Papua New Guinea, Nauru, New Caledonia, Tuvalu and Kosrae.
It said people near impacted coastal areas should stay alert and exercise normal caution near the sea.
American Samoa had issued a tsunami watch following the earthquake but that was later cancelled.
The quake, which hit just before 5am local time on Friday morning, was initially reported to be of magnitude 8 by the US Geological Service but was downgraded shortly afterwards.
