The Seine has been a key focus of attention during the Games ever since it was chosen for the triathlon and marathon swimming - consistently failing water quality tests despite a 1.4 billion euros (£1.2 billion) upgrade to improve the Paris sewerage and water treatment systems.
After an overnight meeting, the international swimming federation World Aquatics and the organising committee said that the athletes' training "would take place as planned on August 7".
On Tuesday, organisers scrapped training in the river for the fifth time since the start of the Games on July 28.
The triathlon was badly disrupted by poor bacterial readings last week, with all swim training sessions cancelled and the men's individual race postponed by 24 hours until Wednesday.
The open-water swimming events, which run for 10 kilometres in a loop around the Seine, are to be held on Thursday and Friday.
If the water is unfit on those days, organisers plan to move the competition to the Vaires-sur-Marne lake where the canoeing events are being held.
