The Paralympics face major budget cuts and, although delayed travel grants will now be paid, 10 countries may struggle to get teams to Brazil.
"The IOC have very full coffers after London 2012," Hugh Robertson was quoted as saying by BBC on Sunday.
"They did much better financially than they would reasonably have expected out of London. They have capacity to help."
Robertson, a former government minister who had day-to-day responsibility for the 2012 Olympic and Paralympic Games in London, added, "The sponsors have the capacity to help. The Brazilian government have a moral obligation to do everything possible."
"My guess is that if this goes wrong they will be in breach of the host nation contract so they are morally and legally obliged to do things."
The International Paralympic Committee said Rio's organising committee has not raised enough money to fund the Paralympics.
Brazil's struggling economy and the fact that only 12 percent of available tickets have so far been sold have been blamed for the shortfall in funding for the Games, which start on 7 September.
Cuts are being made to venues, the workforce and transport, and retired British Paralympian Baroness Tanni Grey-Thompson, who has won 11 gold medals, believes some wealthy nations can also help out.
"Where we are really lucky in the British team is having the resources and set-up to mitigate much of this," Baroness was quoted as saying by 5 live.
"It's desperately disappointing for athletes who potentially can't get there. Maybe some of the better-off countries can step in and do whatever we can."
Organisers were meant to pay travel grants to all 165 participating countries by the end of July. The grants, paid to national Paralympic bodies, cover the travel costs for athletes and officials.
"The support grants should have been paid by the organising committee at the end of July and they have now committed to paying them this week," IPC media and communications director Craig Spence said on Sunday, according to the BBC.
"For 10 countries, those grants may be too late for them to afford their flight tickets - the IPC is working with them this week. If needs be, we will purchase their air tickets in advance and then receive the grant money on their behalf, so we are confident we will have everyone there," Spence added.
