"As of September 18, a final diagnosis has been confirmed for 55 children," Yerbolat Dosayev said.
According to previous reports, two adults and 54 children have been infected with HIV, four of whom have already died.
The minister said only 50% of 9,800 children under two, and all medics who had contact with HIV-infected children, have been examined.
"All medics have tested negative," he said.
Dosayev said medics failed to examine all the donors who gave blood. "Seventeen donors are being sought," he added.
The country's parliament has demanded the resignation of the health minister and health care officials in southern Kazakhstan.
Dosayev said he was ready to offer his resignation. "If it turns out that I am largely responsible, I will have enough courage to resign," he said.
The Kazakh Prosecutor General's office said a criminal case was launched in July.
Prosecutors said they were considering different versions, including violations of blood transfusion procedures, the use of non-sterile instruments and other possibilities.
