Wall Street jumped about 1 percent after the open, spurred by Alcoa Inc.'s bullish outlook for global demand after it reported results late Monday. European shares rose steadily from the start, also gaining on the outlook from Alcoa.

A profit warning from Europe's biggest consumer electronics maker, Philips, which said fourth-quarter profits would be soft due to weakness in its home region, highlighted the contrasting fortunes of the US and European markets.

The euro rose for a second day against the dollar, rebounding from a recent 16-month low, as investors pared short positions. But they remained skittish days before crucial sales of sovereign debt from two of the region's larger economies.

Investors stayed focused on the outlook for the euro zone economy, government debt sales and how the region's banks will raise much needed capital to repair their balance sheets in the wake of poor reception for UniCredit's rights issue.

The euro was up 0.25 percent at $1.2797, underpinned by a solid Austrian bond sale little influenced by the country's heavy exposure to Hungary and by data showing a surprise jump in French industrial output in November.

A well-received Greek bill auction, lower euro zone spreads and news that Fitch ratings agency is unlikely to downgrade France in 2012 also boosted sentiment and the euro.

"Recent developments seem to suggest that activity in the biggest EMU countries is not on the verge of a full-blown collapse," Annalisa Piazza, economist at Newedge strategy, said.

The Dow Jones Industrial Average was up 121.28 points, or 0.98 percent, at 12,513.97. The Standard & Poor's 500 Index was up 15.71 points, or 1.23 percent, at 1,296.41. The Nasdaq Composite Index was up 35.89 points, or 1.34 percent, at 2,712.45.

The key FTSEurofirst 300 stocks index was up 1.8 percent at 1,027.17 points, with gains led by mining stocks, while MSCI's all-country world equity index added nearly 1.6 percent, helped by earlier gains in Asian markets.

The positive sentiment from Alcoa spread to the European STOXX Oil & Gas index, which hit a 10-month high and extended a rally that began at the start of the year, to be up 1.1 percent on the day at 352.4 points.

"A good start to the earnings season; it shows the demand outlook is not so bad and we could get more positive surprises," Mike Lenhoff, chief strategist and head of research at Brewin Dolphin Securities, said.

US government debt prices fell as stocks rallied and reduced jitters about Europe pared safe haven demand for bonds ahead of a $32 billion auction of three-year notes.

The pullback in the Treasuries market was modest. Benchmark yields remained stuck in the 2 percent area on expectations that slow growth and low inflation would prevail in the United States and the euro zone debt crisis would continue.

"The 'risk-on' sentiment is weighing on bonds and the upcoming supply argues for a steeper yield curve," said Carl Lantz, chief US interest rate strategist at Credit Suisse in New York.

The benchmark 10-year US Treasury note was down 10/32 in price to yield 1.99 percent.

Brent crude oil rose to above $113 a barrel as tension over Iran's nuclear program and unrest in Nigeria outweighed persistent concerns about the strength of Europe's economy.

Brent crude oil rose $1.07 a barrel to $113.52 a barrel. US crude oil was up $1.67 to $102.98.

Spot gold prices rose $26.14 to $1,637.10 an ounce.