The U.S. and Europe promise more sanctions as explosions ring out in Kyiv and other cities.
US markets followed overseas, with Germany's Dax down 4.8% and Asia's Hang Seng index down 3.2%.
The fall in the Dow came after Wednesday's 465-point fall as investors caught hold of the reality that Putin would not be deterred from declaring "a special military operation" in Ukraine. There were reports of explosions and other military activity in the capital of Kiev and other cities as Russian forces attacked Ukraine from the west, south and north.
Ukrainian President Volodymyr Zelensky on Thursday declared martial law and announced that the country had severed diplomatic ties with Russia, while urging the Russian people to speak out against the war.
"But if we are attacked militarily, if they try to take away our freedom, our lives, the lives of our children, we will defend ourselves," he said in a video address. "When you attack, you will see our faces, not our spines, our faces."
President Joe Biden condemned the aggression and plans to speak to the nation on Thursday. Several other governments joined in criticizing Putin's move, which was telegraphed for several days, and an EU meeting was due later.
"Russia alone is responsible for the death and destruction caused by this attack, and the United States and its allies and allies will respond in a united and decisive manner," Biden said.
The US and Europe have pledged further sanctions against Russia and key Putin supporters after initial sanctions announced earlier in the week.
World energy markets were also hit by the attack, with the price of a barrel of oil above $100. Russia in particular is one of the major suppliers of oil and natural gas to Europe, and it is unclear whether other producers such as Mexico, Canada and the Gulf states will increase production.
The sell-off comes as investors are already worried about rising inflation and the Federal Reserve's plan to raise interest rates early next month. The price of gasoline has been a major contributor to the overall rise in consumer prices, which are currently up 7.5% compared to a year ago.
If Russia succeeds in controlling Ukraine, or disrupting its economy, it could have consequences beyond energy markets. The country is a major supplier of major metals such as uranium, titanium and manganese, while it is also a major agricultural producer of barley, potatoes, rye and wheat.