It announced on Friday that airline Emirates would sponsor the Spinnaker Tower in a Â£3.5m deal.
Over the weekend, nearly 10,000 people signed an online petition against plans to repaint the tower, which is currently white.
Red and white are the colours of nearby Southampton's football club, Portsmouth's major rivals.
Council leader Donna Jones said she had been "extremely worried and concerned" about the strong public response against the plans.
She said: "I am passionate about this city. I was born here and have lived here all my life... Likewise I love Portsmouth Football Club, the Royal Navy and our heritage. I fully understand people's feelings about blue being the city's colour and the city emblem.
"I am pleased to advise that, after working with Emirates over the weekend, and having spoken to Mark Catlin, chief executive of Portsmouth FC, and other key stakeholders, we are working up a new design for the tower. The design will reflect the city's heritage."
The tower is due to be renamed the Emirates Spinnaker Tower. The revised design will be made public in the next few days.
The branding is due to be in place in time for the America's Cup World Series sailing event in July and will remain in place for five years.
The petition against the changes said: "To allow the colours of Southampton to stand tall on one of our city's most prominent landmarks shows an incredible lack of empathy for the residents. It must be stopped."
Paul Andrews, who describes himself as a Southampton FC supporter on his profile, wrote on Twitter: "All it needs now is the #SaintsFC badge at the top."
The colours of Portsmouth Football Club are blue and white.
The 560ft (170m) tower opened in 2005. It is owned by the council but run by a private company.
Portsmouth City Council has promised to review plans to paint a city landmark red and white.