The idea has been criticised by descendants of the tower's designer Gustave Eiffel and has sparked unease among some Parisians.
The proposed addition is also expected to run into complex regulations designed to protect historic buildings.
"The idea is to make permanent the events that Paris has lived through," deputy mayor Pierre Rabadan, who is in charge of sports, told AFP.
"The Olympic Games are also a symbol of peace, fraternity and, whatever people might say, they (the Paris Games) will have marked the history of the city and probably the history of the Olympic movement," he added.
The logo "does not modify the architecture of the tower. The tower continues to evolve with time," he said, referring to the addition of a new telecoms antennae at the top of the "Iron Lady" in 2022.
"We're not disfiguring anything. We are going to add a powerful symbol to this iconic structure and this historic Parisian monument," he said.
A giant Olympics logo was erected on the tower before the July 28-August 11 Olympics and it became a popular backdrop for selfies by visitors.
Mayor Anne Hidalgo announced on Saturday that she intended to take down the five interlocking rings, which are too heavy to remain on the monument, and replace them with new lighter versions.
A technical study is currently being financed by the International Olympic Committee into the replacement rings and the Switzerland-based non-profit might end up paying for the final versions, Rabadan said.
The final design is expected to result in a logo of roughly the same size as the existing one, but its prominence might be reduced at times -- although Rabadan said it was too early to say how.
"The idea is that they are visible when we want them to be and sometimes they will be less so," he told AFP.
A petition on Change.org against the idea had gathered 34,000 signatures by Tuesday evening.
"When you take decisions like this, you're always faced with criticism from people who don't want things to change," Rabadan said.
The Association of Gustave Eiffel's Descendants said Sunday that it was against the idea of the tower becoming an "advertising outpost".
The association as well as opposition Paris MPs and councillors urged Hidalgo to consult Parisians and residents around the tower more widely.
