(CNN) Numerous rivers in the Southeast are overspilling their banks after recent heavy rains, and communities along the lower Mississippi River in particular have days to go before they see the worst of it.

In Louisiana, Gov. John Bel Edwards declared a state of emergency Friday because the threat of more rain in the region and more flooding along the Mississippi.

The US Army Corps of Engineers this week opened Louisiana's Bonnet Carre Spillway to divert rising water away from New Orleans to sparsely populated areas. In the capital, Baton Rouge, the river already was at more than 41.28 feet -- more than 1 foot above major flood stage -- and it could rise another 2 feet over the next two weeks, the National Weather Service says.

"We anticipate some parishes may need assistance dealing with these conditions and the state stands ready to offer that support," Edwards said.

The river, already at flood stage in areas from Missouri south into Louisiana and Mississippi, isn't expected to crest in many of those places for days.

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