They are Bang Ban, Phra Nakhon Si Ayutthaya, Sena, Phak Hai, Bang Pa-in and Bang Sai districts.
Mr Witthaya said he had sent an urgent order to district chiefs and local administrations to watch and provide assistance for affected riverside communities as needed.
Overflows from the Chao Phraya river have swamped Wat Boonkannawas in tambon Sai Noi of Bang Ban district where construction of a floodwall around the temple has not yet been completed.
A camp area for construction workers and heavy machinery has been inundated.
Royal Irrigation Department director-general Lertviroj Kowattana said the high water level in the Chao Phraya River is caused by days of continuous heavy rain but the situation is still under control.
At its peak on Tuesday morning, the water level of the Chao Phraya in Kamphaeng Phet province was measured 161.40mm.
The water flow rate from the Chao Phraya dam towards Chai Nat province was 1,800 cubic metres a second, Mr Lertviroj said.
"At this rate, areas at the end of the dam won't be affected except for some low-lying areas where flooding usually occurs every year," he said.
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Sukhothai people hit by flooding. (Photos by Thiti Wannamontha)
Science and Technology Minister Plodprasop Suraswadi said he, as chairman of the government-appointed Water and Flood Management Commission, wanted to apologise to the people of Sukhothai after the flood swollen Yom River broke through eroded levees beneath flood walls and swamped parts of the city.
"I would like to say sorry to the Sukhothai people as I was not able to know about the eroded levees," Mr Plodprasop said. "I've ordered officials to quickly repair them."
The flood situation in Sukhothai was stabilising and the water level should begin to recede over the next couple of days, the minister said.
He said Prime Minister Yingluck Shinawatra had instructed officials to inspect old flood walls to prevent a recurrence of the problem in Sukhothai.
State Railway of Thailand deputy governor Kamol Tangkijcharoenchai said repairs have been completed on the flood damaged rail track in Lamphun province.
Full services on the line north to Chiang Mai resumed on Tuesday afternoon following tests on the safety of the repaired track.
Meanwhile, Thai netizens have come up with a flood-related competion they call the Tharalympics (thara means water in Thai) following news of flooding in the provinces.
In the Tharalympic games, people have to race against the surging water by doing various activities such as lifting their belongings to higher ground, piling up sandbags, storing food and walking through flood water.
In 2011, Thailand was hit by the country's worst flooding in 50 years. The GDP shrank 10.7% in October-December of last year from the previous quarter.