Shipping operations at the port were suspended and the Mauao base track was closed as a precaution while the ship was urgently towed away to a safe anchorage in deep water outside Tauranga Harbour, aided by tug boats.
The Funing will not return to port until authorities give permission.
The ship's hull is understood to be intact and there was no pollution.
The Transport Accident Investigation Commission and Maritime New Zealand are investigating the incident.
The commission's investigation will focus on the causes and circumstances of the incident and the Maritime NZ investigation will focus on whether the rules were followed correctly.
Maritime New Zealand's deputy director of safety response systems, Nigel Clifford, said an inspection dive could not be done yesterday due to the weather and sea conditions, but it was hoped this would happen today.
"If the vessel is safe to sail without repairs it will be able to continue its planned voyage to China.
"If the vessel requires repairs a repair plan will be established by the owners. Authorities would overview any such proposals."
It was not possible to say how long the vessel could be in Tauranga.
Commission spokesman Simon Pleasants said a team of three investigators had arrived in Tauranga from Wellington.
The log carrier that lost power at the entrance to Port of Tauranga this morning is now safely anchored in deep water outside Tauranga Harbour. The final update from @Portoftauranga can be found here: https://t.co/kT4TwHuNOm
— Maritime New Zealand (Nō te rere moana Aotearoa) (@MaritimeNZ) July 5, 2020
A Port of Tauranga spokeswoman said the incident delayed the arrival of one container ship and one log ship, but there were no long-term impacts on port operations.
"We frequently deal with shipping delays and changes due to weather and other operational reasons."
She said the marine teams did "an amazing job in keeping the stricken vessel steady and then towing it to safety".