"Where our staff can, they're repairing damaged service lines," she said.
People without power or hot water after the main supply line to their suburb or street was reconnected should get in touch with Vector by phone or app, as there could be localised faults on individual properties, she said.
Restoring hot water is separate to power restoration, and has been restored at the suburbs at the bottom of this page.
Remaining suburbs will be restored progressively this week.
Outage crews will continue working 24/7 until everyone is connected, Vector says.
Vector's list of estimated restoration times shows most remaining properties will have power restored this week.
The latest date for restoration work is Sunday, for Browns Bay, Devonport, Greenhithe, Parkhurst, Silverdale, Sunnyvale and Takapuna.
Trees weakened in the storm are continuing to give way, and Vector says people should be wary around large trees or branches over the next few weeks.
If people see a tree with damaged branches that haven't come down, they should alert the landowner or Auckland Council.
All downed power lines should be treated as live, and people should stay well away and not cut or move trees that are in contact with lines.
People who use medical equipment that relies on electricity should let their power company or retailer know first. Contact Civil Defence on 0800 22 22 00, if that is not possible.
If there is an immediate health threat, contact a health provider or call 111.
Vector is working with Civil Defence and Auckland Council to provide assistance to impacted communities where they can.