* Euro steadies after tumble caused by ECB policy decisions
* Shared currency tops $1.36
* Stocks, Treasuries rally (Adds Treasuries rise, latest prices)
NEW YORK, June 5 (Reuters) - The euro turned higher on Thursday, bouncing back from losses caused by European central bankers rolling out sub-zero interest rates in a battle against low inflation, while Wall Street and U.S. Treasuries prices rallied.
The euro, a common currency used by 18 countries that a month ago traded at a hair under $1.40, on Thursday last stood at $1.3633, up 0.25 percent on the day and far from a four-month low of $1.3504 touched earlier.
The euro is down nearly 1 percent so far in 2014 against the dollar, which was off 0.2 percent on Thursday against the Japanese yen and 0.40 percent against the British pound at $1.6800.
The dollar index, which measures the dollar against a basket of currencies, was initially up and brushed a high last seen on Feb. 7 before easing 0.22 percent.
In a bid to boost the euro zone economy and avoid Japan-like deflation, the European Central Bank cut its interest rates to record lows, introduced fees in the form of negative interest rates on overnight depositors, and offered banks new long-term funds.
Policymakers stopped short of large-scale asset purchases for now, but ECB President Mario Draghi said more action would come if necessary.
Euro zone shares rallied, led by banks and peripheral indexes, as the ECB policy announcement lifted the German blue-chip DAX index to an all-time high of 10,013.69, before it ticked back down to 9,967.01, an overall increase of 0.4 percent on the day.
"This is very positive for equities because implicit in the announcement is that rates are going to be low for a very long time," said Manish Singh, director and head of investment services at Crossbridge Capital.
In New York, Wall Street rallied and took the Standard & Poor's 500 index of top American companies to an intraday high for the seventh time in eight trading sessions. The Dow Jones industrial average rose 100 points or 0.60 percent, to 16,836.40 as the S&P 500 gained 13 points to 1,940.32.
"The ECB is providing stimulus and that will help the global economy. It's a powerful force in keeping world interest rates low," said Kathy Jones, fixed income strategist at Charles Schwab in New York. "Draghi delivered."
Prices of U.S. Treasury securities rose in choppy trading. Benchmark 10-year notes were last up 8/32 in price to yield 2.58 percent, the same as before the ECB decision that initially lifted yields.
"It probably puts pressure on U.S. rates to the extent that it's putting pressure on risk-free rates in Europe," said Chris Diaz, a portfolio manager at Janus Global Bond Strategy in Denver, Colorado. (Additional Reporting by Karen Brettell, Rodrigo Campos, Richard Leong and Daniel Bases in New York; Editing by Chizu Nomiyama and Meredith Mazzilli)