Volatility gripped Wall Street on Tuesday.

The Dow plunged more than 392 points, or 1.6%, on fears about political turmoil in Italy and renewed trade uncertainty between the United States and China. It was the worst day for the Dow since April 24.

The S&P 500 and the Nasdaq slipped 1.1% and 0.5% apiece.

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Italy is headed for new elections, and investors worry the result could throw the European Union into turmoil. Investors soured on Italy's debt, demanding higher yields in return for taking on added risk.

The tension in Italy spread to US markets. In Wall Street's worst-case scenario, Italy, the third-largest economy in the European bloc, would vote to leave the euro.

"It's got the earmarks of a disgruntled Italy," said Arthur Hogan, chief market strategist at B. Riley FBR. "We've gotten to the point now where it's catching people's attention."

The White House also announced Tuesday that it would impose 25% tariffs on $50 billion worth of goods from China and place new limits on Chinese investments in the United States. The move caught investors by surprise. Treasury Secretary Steven Mnuchin said a trade war with China was "on hold" less than 10 days ago.

Signs of alarm showed up across the market on Tuesday.

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The VIX (VIX), Wall Street's fear gauge, spiked nearly 31% to its highest level since May 4. CNNMoney's Fear & Greed Index pushed into fear territory. A week ago, the index was flashing greed.

Investors rushed to safety in bonds. The yield on the 10-year US Treasury fell sharply to 2.77%. Yields move in the opposite direction of prices.

Last month, the 10-year yield crossed 3% for the first time since 2014. Longer-term yields have been climbing steadily as the Federal Reserve raises interest rates. Higher rates dent the value of bonds' fixed payouts.

The bond rally drove a steep bank selloff. Falling yields can make it harder for banks to make money on the interest they charge for loans.

JPMorgan Chase (JPM) dropped 4%, while American Express (AXP) and Goldman Sachs (GS) lost 3% to drag the Dow lower. Morgan Stanley (MS) and State Street (STT) were the worst performers on the S&P 500.

As yields fell, investors headed to higher-dividend stocks such as utilities and real estate.

Coca-Cola (CCE)was the only company on the Dow to finish the day ahead The Dow Jones Utilities Average (DJU) closed up too.

"It's a typical risk-off kind of day," Hogan said.

Meanwhile, a drop in oil prices put pressure on energy stocks.

Oil prices have slumped around 10% since Saudi Arabia's energy minister said on Friday that Saudi-led OPEC and Russia would pump more oil. US crude dipped 1.6% to a little below $67 a barrel.

--CNNMoney's Matt Egan contributed to this story.