By Richard Leong

NEW YORK (Reuters) – U.S. and European stocks rose on Tuesday, rebounding from heavy losses tied to anxiety about tumbling oil prices and Greece possibly leaving the euro zone, while nervous investors bought more gold, yen, low-risk government bonds and other safe-haven assets.

The oil market rout has continued into early 2015 with Brent crude futures falling to near $ 51 a barrel, or 5-1/2-year lows. This intensified concerns about how the dramatic price drop due to sluggish global growth and a supply glut will hurt earnings of oil companies and exacerbate disinflationary pressure worldwide.

“Global risk sentiment has been hurt by sliding stocks and oil prices. That is leading to a perception that there is a lack of demand, and that has implications for global growth,” said Jeremy Stretch, head of currency strategy at CIBC World Markets in London.

Greece’s anti-bailout party Syriza held a slim lead in polls before the Jan. 25th national election, which rekindled speculation whether the euro zone might let the country leave the economic block rather than renegotiate Greece’s international bailout.

Data on Tuesday showed euro zone’s manufacturers saw almost no growth in the fourth quarter, putting pressure on the European Central Bank to take bold steps to avert the region from slipping into recession.

U.S. and European equity markets achieved some stability on Tuesday after Japanese shares posted their worst one-day drop in 10 months overnight <.N225> and Wall Street booked its worst session in three months on Monday.

In early U.S. trading, the Dow Jones industrial average <.DJI> rose 36.73 points, or 0.21 percent, to 17,538.38, the S&P 500 <.SPX> climbed 3.98 points, or 0.2 percent, to 2,024.56 and the Nasdaq Composite <.IXIC> advanced 2.32 points, or 0.05 percent, to 4,654.90. [.N]

FTSEurofirst 300 index of top European shares <.FTEU3> was up 0.3 at 1,336.79 points. [.EU]

The MSCI world equity index <.MIWD00000PUS>, which tracks shares in 45 nations, fell 1.36 points or 0.33 percent, to 406.65.

Investors poured more money into top-rated government debt, driving the average of yields on German , U.S. and Japanese 10-year debt to less than 1 percent for the first time.

Ten-year Bund yields fell to record low of 0.442 percent, while 10-year Treasuries yield fell below 2 percent for the first time since mid-October. [US/] [GVD/EUR]

The dollar dipped to as low as 118.65 yen from Monday’s high of 120.68, retreating from a seven-year peak of 121.86 set last month. The euro fell more sharply against the yen to 141.39 yen , a two-month low. [FRX/]

Gold hit a three-week high on safe-haven bids, and last traded up $ 6.50 or 0.54 percent, to $ 1,210.20 an ounce. It struck earlier Tuesday a session peak of $ 1,214.40, its highest since Dec. 16. [GOL/]

In the oil market, Brent crude was last down $ 1.07, or down 2.01 percent, at $ 52.04 a barrel. U.S. crude was last down $ 1.01, or down 2.02 percent, at $ 49.03 per barrel.

(Additional reporting by Patrick Graham, Anirban Nag, Emelia Sithole-Matarise, Jamie McGeever, Jan Harvey, Libby George in London and Hideyuki Sano in Tokyo; Editing by Kevin Liffey and Nick Zieminski)