Wednesday's debate also dealt with the process for determining which sports are in the Olympics and whether to lift the current cap of 28 sports and 10,500 athletes for the Summer Games.
No final decisions are being taken at the IOC session, or general assembly, in Sochi. Proposals will be formulated after the games and put up for a vote at a special meeting in Monaco in December.
However, the opening morning of debate provided a sense of the key issues and the general trend of opinion among the 100-plus members.
IOC vice president John Coates said the members should consider whether countries rather than cities should bid for the Olympics and whether to allow joint bids from different countries or cities.
Under IOC rules, a single city bids to host the Olympics. Joint bids are not permitted.
The possibility of changing the system drew a mostly negative reaction, with members stressing that the Olympics enjoy a special status of taking place in one city.
"One of the unique aspects of the Olympic Games is the unity of time and place," Canadian member Dick Pound said. "It's not an event made in a television studio. It's what happens on the ground. We should be very careful about destroying that."
The view was echoed by Israeli member Alex Gilady.
"If we go to a country, we will lose the Olympic Village," he said. "The Olympic Village is perhaps the most important uniqueness of the Olympic Games. Maybe it could be done in the Winter Games, but in the summer if we change the concept from city to country we may start the end of the games."
Two athlete members, Australian rower James Tomkins and swimmer Kirsty Coventry of Zimbabwe, also opposed any change. Coventry said athletes would lose the "level of competition" they are used to in a single host city.
Many members spoke in favor of reinstating visits to bid cities in a controlled system paid for and organized by the IOC. Visits were banned in 1999 in the wake of the Salt Lake City bid scandal which led to the ouster of 10 members for accepting cash, scholarships and other inducements.
Several members said it was impossible to get the full grasp of a bid without seeing the city with their own eyes, rather than through promotional books and videos.
"It's very difficult to look at the mirror and vote for a city you have never seen and never visited," Gilady said. "Videos can make everybody so pretty and so beautiful."
The lone dissenter was Prince Albert of Monaco.
"I think it's very risky even if it's done in a very organized and controlled fashion," he said. "The costs are significant for the IOC and it's also a lot of time for the bidding city to organize these visits and make sure everybody gets to see what they want to see. It's a very difficult issue. I think it's very risky to go down that path again."
On the Olympic sports program, Bach is pushing for flexibility to allow more sports to get into the games, possibly by cutting some existing disciplines and events. Whether to keep the limit of 28 sports and 10,500 athletes remains an issue.
"I have lately finished reading the Bible and it's not written that we must have 28 sports and 10,500 athletes," Gilady said. "For too long we have locked ourselves behind the bars for seven years with too little flexibility to change for the benefit of sports and athletes."
Also put up for debate:
• Extending the 17-day Summer Games schedule to allow for three full weekends of competition.
• Adding more mixed events. Tennis and badminton currently have mixed doubles, and men and women compete against each other in equestrian. Swimming has mixed relays in its short-course world championships.
• Cutting classification or non-medal consolation events, such as those currently held in basketball, rowing, field hockey and water polo.
• Rotating athletes out of the Olympic Village once they've finished competing to allow athletes from other sports to come in. This idea drew opposition from several members, including former Olympic ice hockey star Angela Ruggiero of the United States.
AP Sports Writer Graham Dunbar contributed to this report.
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