The latest outbreak has been blamed on the H5N1 virus, leading to a health scare around Asia, which is already on the brink after the re-emergence of SARS in southern China.
Tran Phan Duong, deputy director of the Central Paediatric Hospital in Hanoi - one of the two hospitals monitored by the WHO - said on Sunday nine patients had bird flu symptoms and were undergoing tests for the virus.
More than two million chickens have died or have been killed in Vietnam and the government has banned the sale of poultry in Ho Chi Minh City, its largest metropolis.
There are no exact figures on the number of provinces and cities affected by the virus, but the ministry of agriculture and rural development said last week that nearly half had reported outbreaks.
"We are not sure how good a handle they have in the centre of the country," Bob Dietz, the World Health Organisation's spokesman in Vietnam, said on Sunday.
"We are still trying to understand the extent of H5N1 in Vietnam and are still trying to assess the risk it poses to the human population."
UN team arrives
A two-member team from the WHO and the Food and Agriculture Organisation (FAO) arrived in Ho Chi Minh City late on Saturday on a week-long mission to assess the situation.
The WHO says there is no proof
of human-to-human transmission
Ten more experts from the two UN agencies, as well as the US Centres for Disease Control and Prevention are due to arrive in Vietnam this week.
According to WHO, a large number of people have been admitted to two hospitals in Hanoi, complaining of respiratory problems, but it was too early to say if they were victims of avian influenza.
The UN health agency also said there was still no evidence of human-to-human transmission.
The four people confirmed to have died from the H5N1 virus caught it directly from an infected bird.
However, the WHO has warned of dire consequences if the virus mutates.
The four victims included a mother and her young daughter, from the northern province of Ha Nam province.
The other two, both children, were from Nam Dinh and Bac Ninh provinces, also in the north.
No confirmed or suspected deaths have been reported in South Korea, Japan and Taiwan, which are all coping with their own bird flu outbreaks.
Taiwanese authorities on Saturday ordered 35,000 more chickens to be slaughtered after the less virulent H5N2 strain of the virus was found at a second farm in one week.
The WHO says bird flu is largely transmitted through bird droppings and not cooked meat, casting doubt over bans imposed on poultry imports from affected countries by many Asian nations.
The virus circulates in the air and is carried by the wind from fresh droppings of contaminated chickens.