At least 6,770 deaths have been recorded worldwide since the flu virus emerged in April, according to the latest WHO update which showed 520 known fatalities in the past week.
There are "early signs of a peak in disease activity in some areas of the northern hemisphere", the WHO said in a statement.
H1N1 flu is still widespread across the United States although it appears to have recently peaked in most areas except the northeast. But transmission continues to intensify in Canada, with the highest number of doctor visits by children.
Spread of the flu appears to have peaked in western European countries including Belgium, Britain, Iceland and Ireland after a period of intense outbreaks, the United Nations agency said.
Norway and countries further east including Georgia, Lithuania, Moldova and Serbia are reporting sharp increases in influenza-like illness or acute respiratory infection, it said.
Kazakhstan, Uzbekistan and parts of Afghanistan -- particularly Kabul -- are reporting higher numbers of flu cases. Israel is also reporting sharp increases.
"Essentially what is happening is that it is spreading eastwards," Anthony Mounts, medical epidemiologist on WHO's influenza team, told Reuters. "Typically seasonal influenza always starts west and moves eastwards. It seems to be following that pattern except it is coming very early this year."
Flu transmission remains active in east Asia, the WHO said. "In Japan, influenza activity remains elevated but stable nationally and may be decreasing slightly in populated urban areas," it said.
Most countries in tropical areas of central and South America continue to report declining numbers of flu cases, with the exception of Peru and Colombia, it said.