The World Health Organisation sought to allay panic over the spread of the disease as the Turkish government defended itself against accusations that it had not taken enough preventive action.
Results of tests, first done in Turkey and confirmed by a laboratory in Britain, were released hours after a third child from the same family died in the east of the country from what officials said was bird flu.
"Only two of the three people who died have tested positive" for the H5N1 strain of bird flu, ministry undersecretary Necdet Unuvar told a press conference in Ankara.
He said one of the dead children's results had been negative, but did not specify which one, and that another person who had tested positive was being treated in hospital in the eastern city of Van.
The children were 14-year-old Muhammet Kocyigit, who died in Van hospital on Sunday, followed five days later by his 15-year-old sister Fatma.
Earlier Friday, their 11-year-old sister Hulya succumbed after several days in intensive care, said Huseyin Avni Sahin, the hospital's chief doctor.
The sub-type H5N1 is the strain responsible for the deaths of more than 70 people in Southeast Asia and China since 2003, nearly 40 of whom perished last year alone.
The deaths in Turkey are the first known human fatalities outside Southeast Asia and China.
Mr Unuvar said that apart from the one patient confirmed to be carrying H5N1, 19 other people were hopitalised in Van on suspicion of carrying the disease but their test results were not out yet.
Hospital sources said one of the patients was in a "critical condition."
Local officials in the southeastern city of Diyarbakir meanwhile told AFP that six people, including five siblings aged between six and 10, were brought to a local hospital from nearby Siirt province on suspicion of bird flu.
People urged to stay calm
A WHO spokeswoman urged calm.
The disease has been "contained in one province" in the east of Turkey and "there is no need for excessive panic," Fadela Chaib said in Geneva.
She said a team of five WHO experts were arriving in Van to help officials take the right measures to prevent any spread.
Those experts "will also try to see if we are faced with the first case of human-to-human transmission, which would be the start of a flu epidemic," she said.
Humans only contract bird flu if they come into close contact with infected birds, but scientists fear millions around the world could die if H5N1 crosses with human flu strains to become highly contagious.
The Kocyigit family comes from the impoverished remote town of Dogubeyazit where many families depend on poultry breeding for their livelihoods and live close to the animals.
The Kocyigit children were hospitalised last week after coming into contact with ill chickens living in their house.