Brazil’s new sports minister has predicted there will be “close to zero” cases of Zika recorded during the Olympic Games as he mounted a trenchant rearguard action over a host of issues clouding preparations for Rio.

Leonardo Picciani, who recently became the third person to fill the role since March, said he was convinced the Games, which start on 5 August, would be a success despite a backdrop of political and economic turmoil and a range of other concerns from unfinished transport links to doping controversies.

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On a visit to London during which he also met the culture secretary, John Whittingdale, and the mayor, Sadiq Khan, Picciani also promised a crucial extension to the metro would open “a couple of days before the opening ceremony”, that Brazil would finish in the top 10 in the medal table and there would be a last-minute surge in demand for tickets.

Amid the bitter political turmoil that has gripped the country after the president, Dilma Rouseff, stepped down in the wake of a senate vote to impeach her, concern over the Zika virus has jumped to the top of the list of concerns obscuring the run-up to the Games.

Last week more than 100 health experts wrote an open letter urging the International Olympic Committee to move or postpone the Games over the increased risk of spreading the disease that has been linked to microcephaly and other birth defects if contracted by pregnant women.

“The fire is already burning but that is not a rationale not to do anything about the Olympics,” said the signatory Amir Attaran, a professor at the University of Ottawa who wrote an article for the Harvard Public Health Review arguing the spread of the disease should lead to the Games being moved or cancelled. “It is not the time now to throw more gasoline on to the fire.”

Picciani acknowledged the “concern” but pointed out the World Health Organisation had resisted calls for drastic action. “Brazil is not the only country that has the Zika virus, there are over 60 countries that have registered the Zika virus. We are taking measures in accordance with, and are in constant contact with, the World Health Organisation. We have had a very significant evolution in terms of the situation with the insect that causes the virus,” he said.

Picciani, appointed by the interim president, Michel Temer, last month as part of a shakeup of cabinet posts, said public awareness campaigns carried out by the ministry of health had been successful and pointed to an extra 2,000 health professionals and an extra 146 “intensive care ambulances” that would be on standby during the Games.

He said the climate in August had historically meant the lowest number of recorded cases of mosquito-borne viruses such as Zika and dengue fever.

“We hosted 43 test events in Rio with 7,000 athletes and we have not had any case of Zika or dengue. We had a very significant reduction. We had 4,300 cases in April, which fell to 700 in May and there will be another significant reduction in June or July, and in August it will be very close to zero,” he said.

Another issue preoccupying organisers has been delays to the completion of the metro linking Ipanema Bay to the Olympic Park in Barra de Tijuca. The extension was not part of the bid but has come to be seen as crucial in ferrying spectators, volunteers and staff around Rio’s creaking public transport system.

As the Brazilian broadcaster Globo reported that the state government had been temporarily refused £193m in funding to complete the project amid warnings it could not afford to be delayed a single day longer, Picciani said he had been assured that the link would be finished in time.

“It is a project of the state of Rio de Janeiro. They have been assuring us and have been in constant contact with us. They have assured us they will be complete a couple days before the opening ceremony,” Picciani said.

During the Games the metro will be open only to ticket holders and those with accreditation. It will open to the public from September.

The spectre of doping is also likely to hang over the Games, whether or not Russian track athletes are present.

“We would like all the countries to be in Brazil and for every country to be able to participate. However, this is a decision for the International Olympic Committee and we abide by the rules and decisions the IOC makes,” Picciani said.

Two years ago a senior IOC member, John Coates, sparked panic when he said preparations for the Games were the “worst ever” and since then the organisation has been trying to smooth the path to the first Olympics in South America.

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More recently the International Cycling Union has voiced concern about the fact the velodrome has yet to be finished and there are worries about the polluted water in the sewage affected Guanabara Bay where the sailing events will take place.

Picciani said the velodrome would be completed by the end of June and ticket sales for the Olympics were running at 70% of capacity. Half of all tickets for the Paralympic Games had been sold, he said.

“We are starting a campaign across television, radio, print and social media and from then onwards we expect demand for tickets will be much increased,” he said. “There is a cultural feature of Brazilians that leaves things to the last minute. When these Games begin to be very near, they will buy tickets.”

He also insisted there would be plenty for home fans to cheer, with £800m invested in elite sport since the Games were won in 2009 translating to a predicted leap into the top 10 of the medal table from 22nd at London 2012.

Despite conceding the political and economic circumstances were very different from when the bid was won, he pointed to survey figures that claimed 66% support for the Games among Brazil’s population and claimed 79% had said the turmoil would not affect the Olympics.