The confirmation marks the first known case of the deadly bird flu strain in the Arab world.
The H5N1 strain has devastated poultry stocks and so far killed more than 60 people in East Asia.
Mohammed al-Mihana, of Kuwait's Public Authority for Agriculture and Fisheries, told The Associated Press on Friday, further tests on samples from the birds showed that the flamingo found on a Kuwait beach had the H5N1 strain, while a second - a bird imported from an Asian country - had the milder H5N2 variant.
He said the imported bird, quarantined at the airport, was a falcon, not a peacock as reported on Thursday. Both birds were destroyed.
Officials said there were no indications of any bird flu symptoms among humans and they saw no need for any culling of local poultry stocks. Poultry and eggs from local farms were free of the disease, they said.
Al-Mihana said teams would continue to fumigate farms and bird markets, and are surveying locations where birds halt on their migration from Asia to Africa.
Migratory birds have already spread the virus to Russia, Turkey and Romania. But the flamingo in Kuwait was the first case of H5N1 reported in the Gulf region.
He had said on Thursday that tests indicated the birds were infected with H5 flu strain, and there was no need for further investigation to determine if it was H1 or H2. He said he did not have the full information about the tests when he spoke to the AP.
The case is the first report of bird
flu in the Arab world
All tests were carried out in Kuwait, he added.
The H5N1 strain has generated fears of a pandemic should it mutate and become able to pass among humans. So far, humans have caught the virus only from infected birds. The H5N2 strain is a mild variant that is believed to cause little illness.
A FAO senior officer of the Rome-based Food and Agriculture Organisation (FAO), John Lubroth, said Kuwait needed to do more testing.
Kuwait has a national emergency plan for fighting the disease. A laboratory has been testing sick birds found by survey teams or members of the public.
Last month, the government banned all wild bird imports, plus imports of poultry from infected countries.
China on Friday reported its fourth bird flu outbreak in chickens in the same province in two weeks, while Vietnam - which has suffered two-thirds of Asia's human deaths from the virus - ordered its military and police to help fight the disease.
China has reported no human cases, but experts say one is inevitable with continued outbreaks in poultry.
The latest case in China brought the country's total number of outbreaks over the past month to seven.
China has reported seven cases
of bird flu in the past month
In Vietnam, Prime Minister Phan Van Khai called on the army and police to help with anti-flu work as new outbreaks were reported despite mounting efforts to contain the virus, state media reported on Friday.
Worst-hit Vietnam has reported two-thirds of the 64 human deaths attributed to the H5N1 strain of bird flu in Asia since it appeared in late 2003.
Elsewhere in Asia, North Korea issued a bird flu alert, exhorting people to unite against a potential outbreak of the disease and calling the task "significant" in raising the "superiority of its socialist system," the North's media reported.
The announcement came a day after Pyongyang issued an "emergency alert," putting chicken farms off-limits to outsiders and requiring feed transport vehicles to be disinfected, according to the North's Korean Central Television Broadcasting Station, monitored by South Korea's Yonhap news agency.
Bird flu hit North Korea early this year, forcing the communist state to cull about 210,000 chickens and other poultry.
In April, the FAO said the outbreak was successfully contained. No new cases of bird flu have since been reported.