All were about magnitude 2.0.
The first one was at 6.22pm and the sixth was at 6.34pm.
GNS Science duty volcanologist Craig Miller said he had located over 95 earthquakes.
"Our analysis of this new swarm confirms its similarity to the May sequence, which was
interpreted as fault movement.
"Based on the May swarm we expect this morning's activity to continue for a few days."
The National Geohazards Monitoring Centre was keeping a close eye on the earthquakes and for any signs of volcanic unrest said Miller.
"There are no changes in volcano monitoring parameters or the level of volcanic activity
at Whakaari (White) Island.
"Our observations are consistent with minor volcanic unrest and the volcanic alert level remains at 1 while the aviation colour code stays at green."