Sitii Fadilah Supari, the Health Minister, told reporters on Friday that a 12-year-old girl who died on 1 March tested positive for the virus.
Earlier, Hariadi Wibisono, who works in the same ministry, said a 3-year-old boy succumbed to the disease.
Both victims were from Central Java province and appeared to have had contact with infected chickens, officials said.
Meanwhile, Taiwan has protested against a World Health Organisation infections map that lumped the island with its rival, China, officially identifying it as a place that has suffered human infections of the deadly H5N1 strain of the virus.
James Huang, the Foreign Minister, told lawmakers on Friday: "Taiwan is not an area affected by bird flu and is certainly not part of the People's Republic of China."
China announced its 10th fatality from the disease on Wednesday.
Taiwan and China split amid civil war in 1949. China claims sovereignty over the self-ruled island, but concedes it does not administer it.
In Geneva, WHO spokesman Gregory Hartl defended the move. "As you know WHO is a member of the United Nations, and the United Nations policy is that there is one China, and Taiwan is a province of China, therefore the entire country has the same colour," Hartl said.