At the close, the Dow Jones Industrial Average had fallen 1.8 percent, the broad S&P 500 index by 2.1 percent and the technology-heavy Nasdaq Composite Index by 2.4 percent.
This means that the year's previous gains on the S&P 500 and Nasdaq Composite Index were erased during the worst stock market day since October.
It was the first trading day after Trump's threat this weekend of import tariffs against eight European countries, including Sweden, from February 1 if the US is not allowed to take over Greenland.
In the EU, there are rumblings about harsh countermeasures in the form of heavy retaliatory tariffs and other measures.
US interest rates rise
On Tuesday, Trump also threatened 200 percent tariffs on French wines and champagne after reports that President Emmanuel Macron is refusing to sit on Trump's so-called peace council.
Interest rates on US government bonds of all maturities rose on Tuesday, partly due to higher inflation expectations in the event of a possible trade war.
From a market perspective, Trump's tariff threats have often been withdrawn in the past when US interest rates have risen. Higher interest rates make it more expensive for the US to borrow money.
The 30-year interest rate in the United States rose 8 basis points to 4.92 percent.
The Danish pension fund Akademikerpension will sell its holdings in US government bonds in January, the fund's investment manager told Bloomberg.
Dollar down - gold up
One of the few gains on Wall Street was in the VIX - the so-called fear index - which measures market anxiety and climbed 7.6 percent during the day.
The heavyweight technology companies with significant international exposure fared particularly poorly. The companies known as the "Magnificent Seven" - all on the list of the world’s ten most valuable listed companies - fell between 1.1 and 4.2 percent.
Stock market and interest rate concerns are also prevalent in Europe, and Japanese long-term interest rates are the highest since 2007.
The US dollar is generally weakening and one dollar now costs 9.13 kronor.
The spot price of gold rose to a new record level, $4,738 per ounce, as investors seek safe havens.
