The head of UNAids, who has been under pressure to resign over his handling of sexual harassment allegations within the agency, has told the Guardian he will not quit, saying that the HIV epidemic is at a crisis point and there is more work to do.

“We have more than 15 million people waiting for treatment. We have many new infections occurring. My job is not yet done,” said Michel Sidibé , the executive director of UNAids, who has spoken about the controversy for the first time.

As the agency published its latest comprehensive report on the epidemic ahead of the International Aids Conference in Amsterdam next week, he said the battle against HIV/Aids was at a precarious stage, with progress against the rising tide of infection inadequate in many countries and money and time running out.

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The report, called Miles to Go, said the target to end the epidemic by 2020 may not be met. There has been some good progress, notably in reducing deaths by getting people with HIV on antiretroviral drugs. There are now nearly 22 million on treatment out of the almost 37 million living with HIV, and deaths have been cut by 34% since 2010.

“But on balance, the world is slipping off track,” it said. “The promises made to society’s most vulnerable individuals are not being kept. There are miles to go in the journey to end the Aids epidemic. Time is running out.”

Sidibé said he was very aware of the particular sensitivity around allegations of sexual harassment within a United Nations agency that purports to champion the rights of women who are at high risk of HIV infection because of their low social status – oppressed and abused and subjected to violence by men. In sub-Saharan Africa, three out of five new infections were among young women, according to the report.

“It is painful for me honestly because UNAids is about protecting those women who face rape and become HIV positive,” Sidibé said.

HIV activists and the whistleblower who alleged sexual harassment within UNAids have demanded Sidibé’s resignation, calling for Theresa May’s government to intervene, as the UK currently holds the chair of the agency’s board.

Martina Brostrom alleged she was sexually assaulted by Luiz Loures, Sidibé’s deputy. She claimed Sidibé tried to bribe her to drop the allegation by offering her promotion. In leaked minutes of a staff meeting the UNAids chief appeared to attack whistleblowers for a lack of ethics.

Sidibé has vehemently denied he mishandled the allegations. “I received the complaint on 7 November 2016 and on 9 [November 2016] I called for an independent investigation,” he said. “The independent investigation body of the WHO [World Health Organisation] told me they couldn’t do it because the complaint came 18 months later. It was time-barred. I applied to waiver this constraint and go for full investigation.”

He has not spoken before, he said, because he had to protect the confidentiality of the victims and the investigation. “So I refused to just come out and say anything, but I want to say that I never covered up. I never mishandled this. If I made any mistake in my address to the staff, I apologise. It was not at all intentional. I’m focusing on the future and I’m committed to zero tolerance. I will do anything to implement the findings of the independent panel.”

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The independent inquiry is looking at the structure and procedures in place in UNAids. Sidibé said he wants the agency to become a model for the rest of the UN to follow. What had happened was a reflection of what needs to change in wider society, he said.

“This #MeToo movement is welcome. It is a wake-up call for all of us. I don’t see any organisation that is immune from this problem. It is deep-rooted in most of the places where people work,” he said.

The HIV epidemic, he said, “is at a precarious point”, with funding 20% short of where it needs to be and people with HIV being put on treatment at a slower pace than before. There has been disappointment that the number of new infections continues to rise, even though people on the antiretroviral drugs do not transmit the disease. “Up to 50% of transmissions are from people before they start on treatment,” he said. In sub-Saharan Africa, those are likely to be older men who would not take the drugs until they felt ill.

“We are at a very difficult moment from my point of view and we need to say that. Otherwise we would be misleading people. It is time for a wake-up call. We can win, but not yet. If we don’t invest in this epidemic we could really have a rebound.”