If the Romanian cases turn out to be the deadly H5N1 virus, they will be the first evidence the strain has spread to Europe from Asia, where it has killed 65 people and millions of birds since 2003. Russia and Kazakhstan have had outbreaks.
The case of bird flu in Turkey is the first of its kind.
Experts fear the H5N1 virus could mutate into one which spreads easily among humans, creating a pandemic that might kill millions. The so-called Spanish flu pandemic of 1918 killed 20 million to 40 million people worldwide.
Ion Agafitei, Romania's chief veterinarian, said three birds had tested positive in the Danube delta village of Smardan after the first cases emerged in another village on Friday.
Further tests, some in Britain, were planned to discover whether the strain is H5N1.
Turkish Farm Minister Mehdi Eker told CNN Turk television on Saturday that 2000 turkeys had died of the disease on a farm in Balikesir province near the Aegean Sea in western Turkey.
All animals on the farm had been slaughtered to prevent the disease spreading.
"Yesterday, unfortunately, we experienced a case of bird flu. But everything is under control. Every precautionary measure has been taken to prevent it spreading," CNN Turk quoted Eker as saying.
A number of people have died
in Asia due to bird flu
The minister gave no details of the outbreak. The figure of 2000 deaths from the bird flu, cited by CNN Turk, appears high for an initial finding on a case.
The farm is near a natural park known for its rich birdlife.
CNN Turk quoted the provincial deputy governor, Halil Yavuz Kaya, as saying the turkeys could have contracted the disease from migratory birds. Animals were barred from going in and out of the village, he said.
Local officials have set up a crisis centre and a health ministry team has gone to the area, CNN Turk added.
In Romania, quarantines were imposed on the two affected villages and five others which had suspicious bird deaths in recent days. No livestock may be taken from the delta to market.
In Ceamurlia de Jos, a few kilometres from the Black Sea, men with white masks poisoned dozens of birds with carbon dioxide before burning them.
"Mysteriously my birds die one after another"
"Nobody dares to eat poultry here after what happened," Mihai Carciumaru, the mayor of the village, said.
"I attended a wedding today and I asked doctors to check whether the guests had poultry on their menu. But it's not the case. They've all decided to eat pork."
Romanian television showed peasants from the village saying large numbers of poultry had died in recent days.
"Mysteriously my birds die one after another. I've lost 45 geese and authorities will kill the rest leaving me with nothing," an angry villager told private station Antena 3.
The Danube delta contains Europe's largest wetlands and is a major migratory area for wild birds coming from Russia, Scandinavia, Poland and Germany. The birds mainly move to warmer areas in North Africa including the Nile delta for winter.
The Romanian authorities banned hunting across the delta, which is home to 14,000 people, and sent medical teams to test for possible human cases.
Bulgaria, which is seen as a potential next destination for the bird flu outbreak, said it had not registered any cases. Veterinary officials said they would travel to the Danube river border region to monitor the implementation of safety rules.
The New York Times said a draft of the US government's final plan for dealing with a flu pandemic showed the country was woefully unprepared.
The document says a large outbreak that began in Asia would be likely to reach the United States within a few months or even weeks and that more than 1.9 million people could die.