The 35 were among 82 samples tested while another 112 samples are in the process of being tested, L Narendranath, Director of state-run Nizam's Institute of Medical Sciences (NIMS) told reporters here.
He has been designated by the state government to brief media on swine flu status.
He said many patients who have tested positive are recovering.
No fresh deaths have been reported in the last 48 hours and the toll so far this month stood at 12 and this season at 21, he said.
Appreciating the role of private doctors and hospitals in responding to swine flu, Narendranath said the government would support them.
The state government is ready to transport patients in '108' emergency vehicles, he said.