Wall Street shares gained ground in rocky trading on the expectation that further rate cuts this week could prop up the ailing US economy.
Analysts say appetite for risky assets, such as shares, has fallen
The benchmark Dow Jones index gained 1.45% or 176.7 points to 12,384, while the broader S&P 500 was also ahead.
But worries over economic growth in Europe and fears over the health of the banking sector after a fraud at Societe Generale hit shares in the region.
The UK's FTSE 100 closed 1.3% lower, while France's Cac was down 0.6%.
Germany's Dax index meanwhile reversed earlier losses to finish at almost the same level as at Friday's close, up 0.03% at 6,818.85.
Analysts said investors were cautious ahead of a Federal Reserve meeting on Wednesday, at which the central bank is expected to cut rates.
Confidence over a sharp interest rate cut from the current level of 3.5% increased after a government report showed new US home sales had slumped at a record pace in 2007.
The hope is that lower interest rates will help banks offer lower lending costs to businesses and consumers and revive economic activity.
"The Fed is focused on public confidence," said Bruce McCain, head of the investment strategy team for Cleveland-based Key Private Bank.
The technology-heavy Nasdaq rose 1% at 2,349, while the S&P 500 index added 1.75% at 1,353.9
But earlier, gloomy sentiment hung over Asian stock markets.
In Japan, the Nikkei 225 had finished down 4%.
Hong Kong's Hang Seng index closed down 4.3%, while Mumbai's Sensex finished 1.1% lower.
Analysts said despite the falls in some markets, the mood seemed calmer after last week's sharp ups and downs.
Last week began with big stock market falls on growing worries over the US economy, only for them to recover later in the week through a $150bn (£76bn) stimulus plan agreed between the US Congress and the Bush administration.
"Investors don't have the appetite to buy stocks now," said Francis Lun, general manager at Fulbright Securities in Hong Kong.
"The market appears to have hit bottom last week but it's still not in a position to keep rising, considering various events pending such as the Fed rate decision," said Koichi Ogawa, chief portfolio manager at Daiwa SB Investments in Tokyo.
Many analysts are expecting a sharp cut in US interest rates when the Fed, the US's central bank, makes its next scheduled decision on Wednesday.
Last week it reduced rates to 3.5% from 4.25% in an emergency move.
Analysts are also waiting for any further economic details in President Bush's State of the Union address late on Monday.
"There's a lot of uncertainty out there: uncertainty over the US economy, uncertainty over China's economy," said Rob Hart, an analyst with Morgan Stanley in Hong Kong.
"People are also worried about contagion in Europe," he added.
"If the US slows down, will it trigger a slowdown in Europe?"