Oil prices jumped more than $1 on Tuesday after Iran threatened to cut off a key oil shipping route through the Strait of Hormuz while world stocks were little changed as a four-day Wall Street rally lost steam.

The euro was stuck near an 11-month low as investors feared thin market liquidity could complicate Italy's plans to raise 8.5 billion euros in capital markets later in the week, renewing pressure on the euro zone.

Trading volumes were low in most markets as traders returned to their desks for the shortened week between the Christmas and New Year holidays.

U.S. crude oil prices shot up $1.59 to $101.27 a barrel as traders feared possible disruptions in supplies from the Middle East. Recent strong U.S. economic data also supported prices, analysts said.

Iran, facing possible sanctions by the European Union over its nuclear program, said it would stop flows through the Gulf strait, which transits crude from Saudi Arabia, Iran, the United Arab Emirates, Kuwait and Iraq.

The geopolitical fear premium with the Iran comments and also the U.S. consumer sentiment rising to an eight-month high make it hard to be short oil during this holiday week, said Phil Flynn, analyst at PFGBest Research in Chicago.

U.S. crude oil futures have been among the top-performing assets in 2011, with gains of about 9 percent year to date.

U.S. stocks were modestly higher as low market liquidity poured cold water on a four-day rally that turned the S&P 500 positive for the year.

Data showing U.S. single-family home prices fell more than expected in October initially weighed on sentiment, but was offset by another report that showed U.S. consumer confidence rose more than expected in December.

We'll probably have a slight drift upwards but there's not a lot of volume, said Doug Roberts, chief investment strategist at Channel Capital Research.com in Shrewsbury, New Jersey. In the absence of any bad news, we could see a drift up over the next four days.

The Dow Jones industrial average <.DJI> was up 25.69 points, or 0.21 percent, at 12,319.69. The Standard & Poor's 500 Index <.SPX> was up 3.02 points, or 0.24 percent, at 1,268.35. The Nasdaq Composite Index <.IXIC> was up 14.49 points, or 0.55 percent, at 2,633.13.

In Europe, the FTSEurofirst 300 <.FTEU3> index of top shares closed practically flat at 990.35 points, with a fall in the stocks of Italian banks weighing on the broader market. Equity markets in Britain, Hong Kong and Australia remained closed.

The MSCI All-Country World index <.MIWD00000PUS> edged up 0.12 percent, but remained down about 9 percent for the year.

The euro traded at $1.3069, little changed on the day and near an 11-month low of $1.2945 -- a level touched earlier in the month.

The single European currency could suffer more selling if Italy struggles to raise money at this week's year-end debt auction, analysts said. The country intends to sell 8.5 billion euros in three- and 10-year bonds on Thursday.

I think there could be some downside risks for the euro. (Thursday's auction) will be more of a test of the market, given that the bonds auctioned are longer maturities, said Sverre Holbek, currency strategist at Danske in Copenhagen.

A further rise in Italian yields should almost certainly be euro negative, and thin liquidity may exacerbate the move.

Italian 10-year borrowing costs were slightly below the 7 percent level that is viewed as unsustainable in the long run for a country facing a national debt of around 120 percent of GDP. It faces around 150 billion euros of debt refinancing in February-April alone.

The benchmark 10-year U.S. Treasury note gained 4/32 in price, with the yield at 2.02 percent.

(Additional reporting by Ryan Vlastelica; Editing by Kenneth Barry and; Jan Paschal)