The president of the Rio 2016 organising committee has insisted it will deliver a “spectacular Games” despite a long list of pressing issues and a prevailing climate of economic gloom and political crisis.

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Carlos Nuzman, who played a key role in winning the Olympics for Rio at a time when it was envisaged as a coming out party for a new superpower, said there had been “no impact from the political and economic crisis in our country”.

After the Guardian revealed this week that French prosecutors had expanded their investigation into corruption in world athletics to include the bidding process for the 2016 and 2020 Games, Nuzman said Rio’s bid was clean. “Rio was not mentioned in this. I have nothing to add,” he said.

With less than five months to go until the opening ceremony however, more than half the tickets are unsold and there are fears over the Zika virus, the readiness of some venues, pollution in the bay that will host the sailing, transport issues and the impact of cutbacks.

But an upbeat Nuzman, appearing at a press conference in London on his way back from a series of International Olympic Committee meetings in Lausanne, insisted that the only budget cuts had been to the “excess”.

“We are not changing anything about the field of play, we are doing everything for the athletes, nothing has been cut,” said Nuzman of the impact of budget reductions that have meant capacities being lowered at some venues and a scaling back of ceremonies and the volunteer programme. “We have not used any public resources. I think we are the single organising committee that can say that. That is a victory, especially in the moment we are living in our country – we are proud of this.”

Nuzman said that the only test event that had been delayed was cycling, owing to a delay in installing the track at the velodrome. But he insisted it was only a fortnight behind schedule. There have been reports that a key extension to the metro line will not be finished. Nuzman pointed to a quote from the state secretary for transport, Rodrigo Vieira, who promised the line would open for “Olympic operations” by July.

Similarly, he said that Dr Margaret Chan, the head of the World Health Organisation, had offered reassurance to athletes and visitors that the Zika virus should not deter them from travelling to Rio. There will be air conditioning in the athletes’ village in order to deter the mosquitos that carry the virus.

With less than a sixth of Paralympic tickets sold and less than half of Olympic tickets, there are concerns that swathes of empty seats could impact on the atmosphere. But Nuzman insisted there would be a late surge in sales and called on sponsors to ensure their tickets are utilised. “Many, many sports [are] already sold out. If we had more, we’d have sold more,” he said. “For the other sports, we have a campaign.

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Brazilians love to buy tickets at the last moment. This happened with the World Cup and other events. I am confident we will have full stands, and I hope sponsors can give the tickets they have to their guests. I think we are in a good way, apart from the problems you mention we have.”

Nuzman also said he would welcome João Havelange, the disgraced 99-year-old former Fifa president who resigned his position as an honorary International Olympic Committee member before an ethics committee verdict could rule on his role in the ISL bribery scandal. “He will complete 100 years on 8 May. I don’t know if he will come, I hope that he can come,” said Nuzman. “He worked on our bid and he invited everybody to come for his centenary. We hope he is in good health.”

He also said that Olympic venues would be inspected weekly for stagnant water, moving to daily during the Games period. “The field of play of the Olympic Games is the other side of the bay,” he said. “The international federation gave the approval and we will keep a very strong team to clean, which will start and continue during the Games.”