South-western Greensburg lies about 100 miles west from Kansas' largest city, Wichita.
Seven people were killed and at least 70 were injured in the storms. Most of the wounded had to be transferred to other towns in the mid-western state because Greensburg's own hospital was among the destroyed buildings.
A search is currently underway for survivors and federal aid has been deployed following Mr Bush's decision to declare the region a disaster area.
Residents have claimed that early warning systems gave them just 20 minutes to seek shelter before the tornado, described as at least a mile wide, struck.
"The most important thing now is for our citizens to ask for the good Lord to comfort those who were hurt," Mr Bush said after attending church in Washington DC.
"I'm confident this community will also be built… and so we will help in any way we can," he added.
The US National Weather Service predicts the region is not out of danger just yet, with "a few strong tornadoes" expected over the central plains this evening and tonight.
Central Kansas, western Oklahoma and the eastern Texas panhandle are among the areas at risk.
Central states in America's tornado alley are just entering the peak tornado season, although some areas of the country see such storms all year round.
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