Algerian Imane Khelif's bout with an Italian opponent that only lasted 46 seconds and Taiwanese fighter Lin Yu-ting's progress in Paris have sparked a row because both were disqualified from last year's world championships after failing eligibility tests. Khelif fights again on Saturday.
The issue has been complicated by boxing's governance structure -- the IOC seized control of the management of the programme from the International Boxing Association because of concerns about the way the body operated the sport.
In a press conference to review the first half of the Paris Games, International Olympic Committee president Bach was asked if boxing should still feature in the 2028 programme in Los Angeles given the problems raised in Paris.
"Very clearly yes," Bach replied. "Boxing is one of the most global sports. Boxing is a sport with high social values."
However, Bach stressed that boxing needed to find new international leadership.
"First of all, we want boxing in the programme of the Olympic Games. This is the target. But boxing can only be in the Olympic Games in Los Angeles if we have a reliable partner," he said.
"So now the national boxing federations, they have to make their choice. It's up to them.
"If they want their athletes to win medals in Olympic Games in a fair competition, with an international federation with a good reputation, with good governance, with a clear anti-doping policy, with financial transparency, then they must find an international federation as a partner for the IOC.
"It is in their hands."
Bach condemned the social media reaction to Khelif and Lin, with some including former US president Donald Trump framing the issue as men fighting against women.
"Everybody in our world apparently feels obliged to say everything about everything without really considering the sometimes very complex circumstances," the German said.
Bach said anyone questioning the two boxers should "come up with a scientific-based new definition of who is a woman and how can someone who is born, raised, competing and having a passport as a woman cannot be considered a woman".
