Instead of soothing investors, Mr. Mnuchin’s comments, along with Mr. Trump’s attacks on the Fed, added to a nervousness already running high as the stock decline continued to accelerate.

Asian markets on Tuesday followed Wall Street lower, led by Japan, which missed another market drop on Monday because of a holiday. Japan’s closely watched Nikkei 225 stock index fell 5 percent on Tuesday and entered bear market territory, meaning it has fallen 20 percent from its high. Shares in China fell by a much smaller amount in thin trading around the region, thanks to holiday-related market closures around the world.

In the United States, investors were also watching the partial shutdown of the federal government amid an impasse between Mr. Trump and lawmakers over his goal of securing financing for a wall on the border with Mexico.

“With everything that’s going on with the administration and all those data points in conjunction with a market that’s already so negative, it’s just pushing everything down,” said Michael Gibbs, director of portfolio and technical strategy at the brokerage firm Raymond James in Memphis.

The idea that the Treasury secretary was calling banks to ensure the financial system was functioning properly, Mr. Gibbs said, “just added to the negative feeling and gave investors another excuse to sell.

Stock trading ended earlier than usual on Monday, at 1 p.m., and markets were set to be closed Tuesday for the Christmas holiday.

On Friday, the tech-heavy Nasdaq entered bear-market territory. It is now down almost 25 percent from its August high after falling 2.2 percent more on Monday.