European stock markets are losing yet more ground
European stock markets were also depressed, despite a second round of central bank action, including a cut in UK interest rates to their lowest level since the 1960s.
The Bank of England trimmed its rates by a quarter point to 4.75%, while the Bank of Japan also lowered borrowing costs. On Monday, the US Federal Reserve, the European Central Bank and several other central banks had sharply cut their interest rates.
Share prices on Wall Street moved in a narrow range with no sign of a repeat of Monday's sell-off, which had seen the largest points fall of the Dow Jones index in market history.
The Dow fell 17.30, or 0.2%, to 8,903.40 and the tech-heavy Nasdaq was down 24.30, or 1.5%, at 1,555.25.
But brokers warned that the markets might not be entirely stable yet.
"We are looking at a lot of uncertainties that will dictate what happens in the market," said James Park of brokerage Brean Murray & Co.
US slide
Monday had been the first day of share trading in the United States since the attacks on the World Trade Center and the Pentagon.
Stocks plunged across the board, with the benchmark Dow Jones index losing 7.1%, its largest one-day points fall in history.
The tech-weighted Nasdaq index fell by 6.8%.
However, as US markets had to "catch up" five days of losses on European and Asian markets, many analysts had forecast a 10% drop in stock prices.
The fact that a market meltdown was avoided appeared to reassure investors.
Rescue package
The markets were boosted by co-ordinated action by the world's leading central banks.
The first move came on Monday, when the US Federal Reserve cut its key rate by half a percentage point. The Fed was followed by the European Central Bank and the central banks of Switzerland, Canada and Sweden.
On Tuesday, the Bank of England joined in, slashing interest rates to a level not seen since 1964. The Bank of Japan, which already has a zero interest rate policy, announced technical changes that made borrowing even cheaper.
Asian relief rally
In Asia on Tuesday, relief at only limited Wall Street losses helped Tokyo's main share index rise 1.85%, with Korean shares adding 3.45%, and Hong Kong stocks closing 2.48% higher.
But trade was nervous, amid fears over the implications of US reprisals, and rumours of a Taleban declaration of a Holy War against America.
"This is a bit of a relief rally, based on the fact that US markets reopened without a hitch and that the falls were not as severe as had been expected," said Raymond Tsui, head of institutional sales at South China Securities in Hong Kong.
"But people are not convinced that we've seen the worst of the losses on US markets."
Shares in export-reliant firms, notably technology companies, were among losers.
Shares in Nintendo, the computer games maker which relies heavily on US sales, slumped 8.3% to 13,400 yen.