The promise was they would swim in the Seine.

So far this year, no Olympian has been able to do so.

After the heavy rains on the weekend, swimming officials at the Paris Games have canceled both familiarization swims for triathletes eager to try out the river before the men’s and women’s individual events set for this week. Each time, poor water quality levels were blamed.

Better news arrived on Monday: Paris 2024 organizers say the hot sun over the past two days most likely means the water will be clean enough on Tuesday morning for competitors to dive in for the first 1.5 kilometers of the men’s race before jumping on their bicycles and then running 10 kilometers.

“We are confident we will be able to hold the competition tomorrow,” Etienne Thobois, the chief executive of the Paris 2024 organizing committee, said at a news conference on Monday. “We have done everything we can to achieve the swimmability of the Seine.”

The city of Paris and its mayor, Anne Hidalgo, in particular, have a lot riding on that promise, and the sight of athletes splashing down the river with the gold dome above Napoleon’s tomb glittering nearby and the Eiffel Tower rising ahead.

The authorities have spent 1.4 billion euros (more than $1.53 billion) on an ambitious, multipronged and labor-intensive plan to clean the Seine — or, more precisely, to prevent filthy water from flowing into it.

They have dug new sewage pipes to homes, connected the city’s refurbished peniches — houseboats — to the sewage system and added special treatments to two upstream sewage plants.