* Weaker Chinese iron ore prices drag down Australian shares

* Euro close to more than 3-year peak on ECB tapering hopes

* Dollar index probes lowest levels since December 2014

* US markets closed for holiday on Monday

By Lisa Twaronite

TOKYO, Jan 16 (Reuters) - Asian shares pushed higher on Tuesday, erasing early modest losses while the euro stood near a 3-year peak on rising expectations that the European Central Bank could pare its monetary stimulus.

MSCI's broadest index of Asia-Pacific shares outside Japan was up 0.4 percent.

U.S. markets were closed for a public holiday on Monday.

Australian shares slipped 0.3 percent, as miners were pressured by weaker Chinese iron ore prices. The materials and mining index dropped as much as 0.8 percent, with mining giants BHP Billiton Ltd and Rio Tinto Ltd each falling over 1 percent.

Chinese iron ore futures tumbled 2 percent on Monday, as stockpiles of the steelmaking commodity at China's ports surged to the highest since at least 2004, with weaker steel prices also adding pressure.

Japan's Nikkei stock index added 0.8 percent as the yen's recent surge took a breather, with expectations for strong corporate earnings underpinning sentiment.

The euro edged up slightly to $1.2261, within sight of its Monday high of $1.2296, its loftiest peak since December 2014.

The euro blipped higher on Monday and German benchmark bond yields hit session highs after European Central Bank rate-setter Ardo Hansson said the central bank could end its bond purchase scheme in one go after September if the economy and inflation develop as expected.

Adding to the euro's ascent, data showed the trade surplus in the 19-country euro area rose to its highest level in eight months, indicating companies were so far weathering the impact of a stronger currency.

"The markets are going to continue on with this trend," said Stephen Innes, head of trading in Asia-Pacific for Oanda in Singapore, referring to the euro's recent gains.

The dollar index, which gauges the U.S. currency against a basket of six major rivals, wallowed at more than three-year lows. It was last down 0.5 percent at 90.541, after dropping as low as 90.279 on Monday, its deepest nadir since December 2014.

Against the yen, the dollar clawed back some lost ground, adding 0.4 percent to 110.97. It fell as low as 110.32 yen on Monday, which was its weakest level since Sept. 15.

Japanese Finance Minister Taro Aso said on Tuesday that he did not see problems with the dollar weakening to around 110.80 yen, but that big swings in currencies would be problematic.