The stock market resumed its free fall Monday on mounting fears about the stalling economy and worries that the government had few options to increase growth, dual concerns that overshadowed the downgrade of long-term United States government debt.

The Dow Jones industrial average fell 634 points, or 5.6 percent, and the Standard & Poor’s 500- stock index dropped 6.7 percent, the biggest retreats since December 2008 in the midst of the financial crisis, accelerating a sell-off that began a couple of weeks ago. The S.& P. 500 is now down 18 percent from its April 29 peak and is nearing official bear market territory, defined as a fall of 20 percent.

The sell-off continued Tuesday in Asia. The Nikkei 225 in Tokyo was down 3.7 percent in afternoon trading, while the Kospi in Seoul fell 6.2 percent. Shares in Australia sank 2.9 percent, and early indicators suggested that other markets worldwide would follow suit. S.& P. futures fell over 2 percent, signaling a lower open for markets in New York.

So anxious are many investors that they poured money into Treasury securities, the debt the government sells to finance its operations. Even though the ratings agency Standard & Poor’s downgraded United States debt a notch from the sterling AAA rating on Friday, judging it a slightly higher risk than before, many still deem Treasuries to be safer than just about any other investment.