By Richard Black
Environment correspondent, BBC News
Amazon deforestation has slowed markedly, the FAO reports
The world's net rate of forest loss has slowed markedly in the last decade, with less logging in the Amazon and China planting trees on a grand scale.
Yet forests continue to be lost at "an alarming rate" in some countries, according to the UN Food and Agriculture Organization (FAO).
Its Global Forest Resources Assessment 2010 finds the loss of tree cover is most acute in Africa and South America.
But Australia also suffered huge losses because of the recent drought.
"It is good news," said the report's co-ordinator Mette Loyche Wilkie, a senior forestry office with FAO.
"This is the first time we've been able to say that the deforestation rate is going down across the world, and certainly when you look at the net rate that is certainly down.
"But the situation in some countries is still alarming," she told BBC News.
The last decade saw forests being lost or converted at a rate of 13 million hectares per year, compared to 16 million hectares in the 1990s.
However, new forests were being planted to the tune of more than seven million hectares per year; so the net rate of loss since the year 2000 has been 5.2 million hectares per year, compared to 8.3 million in the 1990s.
Globally, forests now cover about 31% of the Earth's land surface.
The biggest change has been in Asia which now reports a net forest growth
The biggest losses of forest occurred in Brazil, Indonesia and Australia.
Australia's reduction of half a million hectares per year is principally down to the drought conditions that have covered most of the country in recent years, thought to be a consequence of global climate change.
The Indonesian and Brazilian figures were not such a surprise, with both countries possessing vast tracts of forest and major logging industries; and deforestation is slowing.
"Both Brazil and Indonesia are reporting a significant drop in the loss of forests," said Dr Loyche Wilkie.
"In Brazil it's spectacular, and that's largely because there is a political goal to reduce deforestation by 80% by 2020 and that's supported by the president."
As deforestation has fallen, there has also been an increase in the planting of new forests, particularly in China, leading to a net increase in national forest cover of three million hectares per year.
But the programme - aimed at preventing desertification, reducing flooding and protecting farmland - is due to end in 2020, and if it does, the FAO points out, that will rapidly lead to an increase in the net loss of forest figure.
India and Vietnam have also mounted significant forest-planting programmes, the FAO notes.
UN agencies hope the net rate of loss will be slowed further in coming years if the climate change-related initiative on Reducing Emissions from Deforestation and forest Degradation (REDD) comes to fruition.
The Global Forest Resources Assessment is principally based on data submitted by governments.
Details also include how forests are regulated and how they are used; and here, there are also some encouraging trends, according to Eduardo Rojas, assistant director-general of FAO's forestry department.
"Not only have countries improved their forest policies and legislation, they have also allocated forests for use by local communities and indigenous peoples and for the conservation of biological diversity and other environmental functions.," he said.
"However, the rate of deforestation is still very high in many countries and the area of primary forest - forests undisturbed by human activity - continues to decrease, so countries must further strengthen their efforts to better conserve and manage them."
The FAO is conducting another survey using satellite observations that they hope will provide a much more detailed assessment, and should be published at the end of next year.