The Australian, who was elected to the post at the IOC's 125th session in Buenos Aires this week, said there was no bigger challenge for the organisation than ensuring Rio was ready on time.
"Our biggest challenge is Rio. There is a little over two years to go and there is still so much work to be done," he said in a statement headlined "Rio preparation of critical concern" released through the Australian Olympic Committee.
"We are all concerned. It is not impossible, but they desperately need a more concerted effort with some of the infrastructure projects and venues."
With the clock rapidly ticking before the first Olympics in South America, many facilities in Rio have yet to be completed because of construction delays and soaring costs.
There have also been street protests about the vast investment being made in the Olympics and the football World Cup next year, which is also being held in Brazil.
In an interview with the Australian Broadcasting Corporation, Coates said it was too late to move the Olympics elsewhere.
"No they can't lose the Games," he said "You're really, your hands are tied at this late stage. And you've just got to work with an organising committee and its underwriting government to get the right solutions."
He added: "The money is there in Brazil. It's a wealthy economy. The plan is right.
"But there just doesn't, or we haven't seen yet too much or enough coordination between the three levels of government when it comes to the big construction projects."
Coates' concerns were echoed by other IOC members in Buenos Aires, who said they voted for Tokyo ahead of Istanbul to host the 2020 Games because of the slow progress in Rio and fears of a repeat for the following edition.