Fifty-five triathletes are scheduled to line up at 8 a.m. (0600 GMT) on Tuesday on a floating pontoon next to the Pont Alexandre III and dive into the Seine, marking the first time athletes have competed in the river at an Olympics since 1900.
The women's individual race is scheduled for Wednesday, also at 8 a.m.
Organisers have set aside Aug. 2 as a contingency day for the individual races and Aug. 6 for the mixed relay in case water quality levels do not improve in time.
"They still seem really hopeful for men tomorrow and women Wednesday," said Team Bermuda coach Dan Hugo, the husband of Tokyo gold medallist Flora Duffy.
"But if needs be one or both will get moved to Friday."
Paris 2024 has already had to rejig some schedules, with men's skateboarding delayed to Monday from Saturday due to rain.
A swimmable Seine is a key legacy Games organisers aim to leave behind for Paris residents.
France has invested some $1.4 billion in new wastewater infrastructure to cut the amounts of sewage flowing into the river, and city authorities have announced plans for three swimming sites to open to the public by June next year.
Sunday's training session was also cancelled after tests carried out on Saturday showed water quality did not meet the required threshold.
The running and bike training sessions remain unaffected.
"Given the weather forecast for the next 36 hours, Paris 2024 and World Triathlon are confident that water quality will return to below limits before the start of the triathlon competitions on July 30," organisers said in a statement on Monday.
