One of the worst hit places was Varanasi, where 290mm of rain fell in 24 hours.
The deluge caused the walls of one house to collapse, killing nine members of a family, Srivastava said.
Four others were also killed in the city.
Atul Kumar Gupta, a senior state official, said schools in Varanasi and Barabanki were closed and the Ganges was overflowing on some stretches.
Varanasi is 270km southeast of Lucknow, the state capital.
In the town of Sitapur 24 people were killed when 12 buildings collapsed, Mritunjay Rai, a government official, said. Sitapur is 80km southwest of Lucknow.
"Two girls were buried alive as their mud house fell on them," Rai said.
The meteorological department said more flooding was expected.
'Heavy rains expected'
"A similar pressure area exists over the Bay of Bengal. Under these circumstances heavy rains are expected in the next couple of days," said LC Ram, the director of the office.
Monsoon season lasts from June to September in India and brings rain vital for farming but also massive destruction.
Floods, mudslides, house collapses and lightning kill hundreds every year.
In northeastern India, floods on Wednesday left nearly 80,000 people stranded and dependent on emergency aid for food and water.
Teams used motorboats to take aid to residents in more than 70 inundated villages on Majuli, one of Asia's largest freshwater islands in the Brahmaputra river.