The Dow Jones Industrial Average rose 65.53 points, or 0.30 per cent, at the open to 21,857.73.
On Sunday, Mnuchin on Twitter chronicled the phone call with heads of Bank of America, Citigroup, Goldman Sachs, JPMorgan Chase, Morgan Stanley and Wells Fargo, who confirmed that they face no liquidity issues and "markets continue to function properly".
Trading volume was light during a shortened trading session ahead of the Christmas holiday Tuesday.
"It's already been a roller coaster today", said Craig Birk, chief investment officer at Personal Capital.
Even major retailers, which typically outperform during the holiday quarter, dropped lower on Monday. The Nasdaq skidded 110 points, or 1.7 percent, to 6,222. Generally, investors look for a 20 percent gain from a low point as well as sustained increases over at least a six-month period as signal of a bull market.
After two years of record-breaking performance, the American stock markets are headed for a disastrous December, which may end up being the worst December in history. Firing the Fed chair would undermine global confidence in the US financial system and eliminate the narrative that the Federal Reserve is independent from political persuasion.
On Monday, Trump said: 'The only problem our economy has is the Fed'.
Trump has largely laid the blame for economic headwinds on the Fed, openly criticising its chairman, Jerome Powell, whom he appointed.
Trump once boasted of market gains, now tweets cause drops
"This is a disaster for the Fed, a disaster for the president and a disaster for the economy".
"The question is what is the primary driver of the jumpiness - economic concerns, Fed policy, Trump-Fed conflict, slowing of global growth?" US government debt is approaching $22 trillion. Trump's trade war with China is creating uncertainty for businesses.
"We've gone through situations before where it's absolutely normal for the secretary of Treasury to reach out to the private sector", Quincy Krosby, a chief market strategist at Prudential Financial, told The Wall Street Journal.
Trump said he had confidence in Mnuchin, a "very talented guy" and a "very smart person".
Small said markets are effectively acting like they're in a bear market situation even though there's no signs of a recession.
Bank stocks declined Monday.
Technology stocks, health care companies and banks took some of the heaviest losses in Monday's sell-off. Microsoft fell 2.2 percent to $96.05. This came after a 4.9 percent plunge on Christmas Day. One of the executives said that the reasons for the market jitters include escalating trade tensions between the United States and China as well as the sudden departure of the well-revered Secretary of Defense, James Mattis. That's 18.7 percent below its record close of 26,828.39 on October 3. Brent crude, used to price worldwide oils, declined 2.6 percent to $52.43 a barrel in London.
The pickup in oil prices helped boost energy stocks. The euro advanced to $1.1417 from $1.1405.
The three major indexes are down for the fourth consecutive session, their worst streak in more than three years.
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