Millions of people living along the Mississippi River braced Saturday for flooding as surging water moved south from hard-hit Missouri where heavy rainfall had already caused rivers and streams to spill over their banks.

Major flooding is occurring or forecast in several states along the Mississippi River, the National Weather Service said. The river crested in St Louis, Missouri, on Friday after spilling its banks in several location there.

"Water is still rising in southern Missouri," Missouri Governor Jay Nixon said on CNN. "It was a storm we are still dealing with in emergency management."

Nixon described the flooding as historic, saying the water level was more than 1 metre over previous highs in some places.

The floodwaters were moving downstream on Saturday, prompting flood warnings in Memphis, Tennessee; Vicksburg, Mississippi; and Baton Rouge, Louisiana, the weather service said.

Communities along the river were told to prepare for high water over the coming weeks as a "copious amount of water" travels south, Accuweather said at its website.

"Water levels will continue to rise in Memphis, Tennessee, and Greenville, Mississippi, as well as Baton Rouge, Louisiana, through the second week of January," according to Accuweather. "Residents in these areas will want to be prepared for historic flooding."

ExxonMobil's Memphis Tennessee Terminal has been shut down, a company spokesman said in a statement emailed to dpa. The spokesman said the facility was being closely monitored so that all necessary precautions could be taken.

The flood warnings cover an area where an estimated 8 million people live in 16 states.

Points along other rivers an tributaries feeding into the Mississippi, including the Ohio, Arkansas, Missouri and Meramec, also reported flooding.

Heavy rainfall earlier this week across several south-central and Midwestern states caused the flooding. Thirteen deaths were linked to the storms in Missouri alone, officials in that state said. Those deaths were among 24 throughout the region, news reports said.

It was an entirely different weather picture in the north-eastern US where light to moderate snow continued falling.

Winter storm warnings and winter weather advisories were posted for Maine, northern New Hampshire and downwind of Lake Ontario, the weather service said.

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