With more than half of the 35 million people living with HIV unaware they are infected, the battle is far from over however, said Michel Sidibe, head of UNAIDS.
"If we are smart and scale up fast by 2020, we'll be on track to end the epidemic by 2030, so that AIDS is no longer a public health threat," he told reporters.
"We have a fragile window of opportunity, because what we do over the next five years will determine the next 15."
In a report released ahead of the 20th International AIDS Conference in Australia from July 20-25, the UN agency said AIDS-related deaths dropped to 1.5 million in 2013 from 1.7 million the previous year.
That was the sharpest annual decline since the epidemic's peak in 2004 and 2005, and marked a 35-per cent drop from the 2.4 million deaths seen in both those years.
New infections also fell to 2.1 million last year, down 38 per cent compared to the 3.4 million in 2001.
Africa remains the hardest-hit continent, with 1.1 million deaths in 2013, 1.5 million new infections, and 24.7 million people living with HIV.
UNAIDS said the battle needed to focus squarely on 15 countries which accounted for three quarters of new infections.
Nine are in Africa: Cameroon, Kenya, Mozambique, Nigeria, South Africa, Tanzania, Uganda, Zambia and Zimbabwe.
But the spotlight is also on Brazil, China, India, Indonesia, Russia, and the United States -- where Black women, Hispanics and young gay man are most affected.
Globally, the report said 35 million people were living with the virus in 2013, up from 34.6 million the previous year.
A major problem, Sidibe said, is that 19 million do not know that they are HIV-positive.
To beat the disease, testing must be more widely available, given that tardy diagnosis is a key problem.
The World Health Organization has called for greater efforts to treat gay men, transgender people, prison inmates, people who inject drugs and sex workers, who together account for about half of new HIV infections.
Discrimination is a key factor.
Nigeria criminalised homosexuality in January, and rights groups say people now fear seeking treatment, a test or mere information about HIV-AIDS, whether or not they are gay.
"People live in fear and this has an impact on HIV programmes," said Olumide Femi Makanjuola of the Nigerian group Initiative for Human Rights.
"Since the law passed, the number of people coming to our centre has reduced," he told AFP.
The story has been similar in Uganda.
In Russia, where injecting drug users and their sexual partners are the key group affected by AIDS, stigmatisation and a dearth of needle exchange and rehab programmes are a key problem.
"If Russia doesn't change the way that they are dealing with the AIDS epidemic, they are going to face a much more serious situation in the near future," warned Luiz Loures, UNAIDS' programme chief.
Sidibe lauded South Africa, which a decade ago was still accused of being in denial about AIDS but has since expanded testing and treatment massively.
"If all the countries could have the dynamic we're seeing now in South Africa in the fight against HIV-AIDS, I would be saying without any caution that we'll control this epidemic completely," he said.
Marcus Low, spokesman of South Africa's Treatment Action Campaign, was more cautious.
"We are very uncomfortable with the way they are talking about the end of AIDS. We think it is premature to be talking in those terms," he told AFP.
"We still have over 1,000 new infections every day in South Africa, it is still a crisis," he added.
Global efforts to increase the number of people getting access to life-saving anti-retroviral drugs have advanced fast, with 12.9 million now receiving treatment compared with 5.2 million in 2009, UNAIDS said.
While the hike is impressive, it falls short of a UN target announced two years ago to reach 15 million people by 2015 -- still less than half the number of sufferers worldwide.
"More than half of people in need still do not have access," said Jennifer Cohn of medical charity MSF.
Despite huge progress in funding for the battle against AIDS -- which rose from $3.8 billion in 2002 to $19.1 billion in 2013 -- the UN is still short of its target of $22-24 billion by 2015.
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