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The Waitaki District Council last month said the work was due to begin before August 10.
However, council projects and assets officer Toby Armour confirmed the arrival of the suction dredge vessel New Era from Dunedin "will be subject to suitable weather conditions".
Stage 1 of the two-stage $500,000 project began late last year, when excavators dug a 3m channel at the harbour entrance.
The dredging work was required to be completed before the end of August, to prevent the work spreading marine algae.
Otago Regional Council regulatory general manager Peter Winder said the work was restricted to "between March and August inclusive if the removed sediments are to be deposited on the seabed".
Mr Armour said it would take up to 10 working days to remove the final 18,000cum of the allowable 25,000cum.
This will be the first time since late 2011 the harbour has been dredged.
On February 9, 2017, Jane Marie foundered after attempting to enter Oamaru Harbour, prompting the regional council's harbourmaster to call for signs at the harbour to warn of the "inherent dangers" of entering the harbour and also for formal consideration of the "restoration of the channel shape, alignment and depth" at the harbour entrance.