Bach spoke at a ceremony in the athletes village to urge compliance with the "Olympic Truce," a symbolic resolution urging warring parties to cease hostilities during the games.
"We remember and grieve for the innocent victims of conflict, and especially the recent victims in Volgograd," Bach said. "Our presence here today is a rebuke to those whose motives and goals stand in sharp contrast to the spirit of harmony and global solidarity at these games."
An Islamic militant group from the North Caucasus region claimed responsibility for the back-to-back bombings in late December in Volgograd, about 640 kilometres (400 miles) east of Sochi, and threatened to strike the Olympics.
Russia has mounted a massive security operation to guard the games, which open Friday and run through Feb. 23. Tens of thousands of military and police personnel have been deployed, along with warships, drone aircraft and anti-missile batteries.
The U.N. General Assembly adopted a resolution in November calling for a global truce during the Sochi Games. Similar resolutions have been passed going back to the 1994 Lillehammer Olympics.
"We are not naive," Bach said. "We know our limits."
The IOC leader said the Olympic Village is a symbol of peace.
"Men and women from different backgrounds, different cultures, different religions and different perspectives live side-by-side in harmony," he said.
Bach's use of the term "different perspectives" could be seen as a reference to sexual orientation. The buildup to Sochi has been overshadowed by an international outcry against a Russian law banning gay "propaganda" among minors.
Activists and some politicians called for a boycott of the games over the issue.
"We must never let politics or other outside forces spoil this spirit," Bach said.
Among those attending the ceremony was Russian pole vault star Yelena Isinbayeva, who is serving as the "mayor" of the Olympic Village in the coastal cluster of venues.
Isinbayeva made headlines in August at the world athletics championships when she condemned homosexuality, saying Russians have "normal" heterosexual relations. The next day, she said her comments in English may have been misunderstood and that she is against any discrimination.
Isinbayeva declined further comment Tuesday on the Russian laws butSvetlana Zhurova, mayor of one of the other two athletes villages in the mountains above Sochi, said the issue had been overblown, was unfairly clouding the buildup to the games and she was fed up with fielding questions about it.
Zhurova, the 2006 Olympic speedskating gold medallist , urged activists not to use the Winter Games as a platform for protests.
"For the spectators it is more important who wins than whether he or she is homosexual or not," she said. "This doesn't matter. I'm sure there will be no problems."
Tuesday's ceremony began in embarrassing fashion for the hosts. As Russian Deputy Prime Minister Dmitry Kozak prepared to speak, the plastic lectern collapsed onto the ground.
Bach drew laughs when he said: "We can see that sport can break down walls this morning."
Members of the IOC's executive board toured the Olympic Village, which will accommodate about 2,200 athletes along the Black Sea coast. Two other smaller villages are located in the mountain cluster above Sochi.
Bach chatted with athletes, grabbed some lunch in the cafeteria and played table tennis in the recreation room.
"The village is really magnificent," he said. "What the athletes appreciate is the proximity to the competition venues. I just spoke to a female American speedskater and Russian ice hockey player and the first thing they say is, 'We can walk from here to our training sessions."
Bach has his own room in the village, keeping a tradition started by his predecessor, Jacques Rogge, though he also stays in a luxury hotel nearby during IOC meetings.
"One of the greatest privileges of an IOC president is you can ask for a room in the Olympic Village," Bach said. "It's here where the Olympic spirit lives."
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