"We end the day with heartbreaking news from Eastern Kentucky. We can confirm the death toll now stands at 37, with many more missing," Andy Beshear tweeted. , the Governor of Kentucky.
“Let us pray for these families,” he added.
Mr Beshear said the death toll is likely to rise as relief workers reach flood-hit areas and find more bodies.
Their search was hampered by further rain on Monday and further thunderstorms are expected tonight.
“As if the situation was not difficult enough for the inhabitants of this region, they have rain at the moment”, had regretted the governor during a press briefing earlier in the day.
The National Weather Service has placed most of eastern Kentucky on a flood alert through Tuesday morning and warned of a risk of thunderstorms tonight in the area.
"Heavy rainfall that could lead to flash flooding as well as severe thunderstorms is possible," the National Meteorological Center wrote on Twitter.
The floods, which began last week and are among the most severe to ever hit Kentucky, have turned some roads into rivers, washed away bridges and swept away homes in one of the country's most deprived areas.
Damage to mobile phone antennas complicated rescue efforts and estimating the number of dead and missing.
On Sunday, the governor said bodies would be found "for weeks, many of which will have been carried hundreds of meters".
President Joe Biden has declared a state of "natural disaster" and released federal reinforcements.