The World Health Organization (WHO) says the 60-day goals it set itself for tackling the Ebola outbreak in West Africa have largely been met.
The WHO set a target of isolating and treating 70% of patients and of safely burying 70% of victims in Liberia, Sierra Leone and Guinea by 1 December.
The WHO's Dr Bruce Aylward said only the treatment figure in Sierra Leone had fallen below the mark.
He warned much work was still needed to get to "zero cases".
The WHO's latest report had put the death toll from the Ebola outbreak at 6,928 in the three hardest-hit West African countries.
However, Dr Aylward said hundreds of deaths reported at the weekend from Liberia were "actually non-Ebola deaths... and we will be taking them off".
The WHO later published revised figures, showing 5,987 deaths in Liberia, Sierra Leone and Guinea, with six more in Mali.
Dr Aylward, the assistant director general in charge of Ebola response for the WHO, said the "yawning gap" between disease levels and the capacity to cope had narrowed significantly.
This was a "very very different place than 60 days ago", he said.
Analysis: Mark Doyle, BBC international development correspondent, in Freetown, Sierra Leone
Whenever you read any Ebola statistic, take it with a bucket load of salt. The UN response mission and the World Health Organization base many of their stats on a hotchpotch of numbers from national health ministries, aid organisations and sketchy information their own officials can correlate.
I've often seen statistics claiming an improvement or a decline in a particular area - and then subsequently heard a first-hand report contradicting that. The truth is this crisis is taking place in one of the poorest corners of the world. All three worst-affected countries have bad roads, unreliable electricity supplies, severely under-resourced governments and poorly educated populations.
So don't expect the numbers to add up every time. Foreign aid workers and journalists want things to be neat. Around here they are not. We do know one thing for certain. The number of dead is definitely an underestimate.
"We now believe that two of the three countries - Liberia and Guinea - are currently treating more than 70% of the reported cases and in Sierra Leone they're probably achieving that in most of the country."
He added: "In all three countries it's clear now that more than 70% of the Ebola deaths that we know about are buried safely. And this is because in the past 60 days, the number of safe burial teams has more than doubled."
He said earlier reports from the WHO that suggested less success in meeting the targets had been revised after analysing the data.
Dr Aylward praised changes made by communities in the three countries, and the "strong national government leadership" they had shown.
When asked when the figures for both goals would reach 100%, Dr Aylward said he did not have a crystal ball and that while progress had been made towards reaching the target, the current achievements were "not good enough to stop Ebola".
He warned: "Catching up and isolating cases does not mean you will automatically get to zero - it will need additional measures."
Dr Aylward said there remained hotspots with rising cases, with particular concern for western areas of Sierra Leone.
But he added: "[The capacity to treat Ebola] at district level is strong and getting stronger in Sierra Leone, and that's why I think the prognosis is actually very good."
Earlier, the head of the UN Ebola response mission in West Africa, Tony Banbury, told the BBC there was still a "huge risk" the deadly disease could spread to other parts of the world.
Speaking in Sierra' Leone's capital, Freetown, Mr Banbury said: "It may spread around this sub-region, or someone could get on a plane to Asia, Latin America, North America or Europe... that is why it is so important to get down to zero cases as quickly as possible".
- Bodies still contain high levels of the Ebola virus
- At least 20% of new infections occur during burials, WHO says
- Relatives perform religious rites including touching or washing the body
- Safe burial process involves observing rituals differently, such as "dry ablution"
- Volunteers with full protective clothing are trained to handle and disinfect bodies