Bach's comments came after Rio's Olympic chief Carlos Nuzman brushed aside complaints over power failures and other problems revealed during a gymnastics test event.
Brazil President Dilma Rousseff suffered a humiliating loss in a crucial impeachment vote in the lower house of Congress on Sunday. She is almost certain to be forced from office well before the Olympic Games open in Rio on Aug. 5.
The crisis has paralysed the government as it struggles to revive the economy from its worst recession in decades, casting doubt on Brazil's ability to complete preparations for the event in time.
A federal prosecutor also told Reuters on Monday that a sweeping investigation into corruption in Brazil is targeting more infrastructure projects for the Olympics than previously made public.
Bach, speaking at the assembly of the Association of Summer Olympic International Federations (ASOIF), called on the IOC to show solidarity with Brazil.
"We know the current economic and political situation in Brazil will continue to make final preparations challenging, but I'm convinced, and we are all convinced, that the Olympic Games 2016 will be truly spectacular," he said.
"The Olympic Games enjoy strong public support from the Brazilian people and the organisers can count on the solidarity of the sporting world."
Bach said that staging the Games was a "team effort" and that "the many successful test events which have already taken place are an excellent example of this team work."
POWER FAILURES
"The sport facilities are either completed or about to be finished," he said. "We know from other host cities that the final stretch leading to the Olympic Games is always the most challenging."
"We're all in it together," he added. "If everyone plays their part, I am confident that these games will be a great success."
Earlier, the assembly heard that a gymnastics event being held in Rio this week, partly as a test run for the Games, suffered from power failures, problems with the timing system and power outages when athletes were performing.
International Gymnastics Federation official Ron Froehlich told the assembly that the power outages were potentially a "serious issue" and also complained of a lack of sufficient lighting in competition and training halls, which he blamed on funding problems.
But Nuzman, in his address to the assembly, said: "Test events are there to detect problems raised by athletes and national federations."
Nuzman also sounded a relaxed note about the political situation.
"Until today we have no involvement and no problems with any of the political or economical situations in the country," said Nuzman, head of the Rio organising committee.
"We are not involved in this and the Games will run normally as they have until today. We don't expect any problems in delivering the Games."
"I have no doubt we will deliver an incredible Games but it is important to remember the situation is completely different today," he said.
Brazil was awarded the Olympics in 2009 when it was enjoying a period of strong economic growth but has since fallen into its worst recession in decades. Brazil is also battling an outbreak of the Zika virus, which is linked to birth defects in newborns.
(Writing by Brian Homewood; Editing by Gareth Jones/Toby Davis)
