* Euro gains after tumble caused by ECB policy decisions
* Shared currency tops $1.36
* U.S. stocks touch new highs as Treasuries rally (Recasts, adds Wall Street record highs and late prices)
NEW YORK, June 5 (Reuters) - European central bankers boosted world markets on Thursday by rolling out sub-zero interest rates and other anti-deflation measures that lifted the euro, U.S. Treasuries, and equities on both sides of the Atlantic.
The euro, a common currency used by 18 countries that a month ago traded at a hair under $1.40, initially sank on news of the European Central Bank's program. But late on Thursday the euro stood at $1.3662, up 0.50 percent on the day and far from a four-month low of $1.3504 touched earlier.
The euro is down nearly 0.70 percent so far in 2014 against the dollar, which was off 0.33 percent on Thursday against the Japanese yen and 0.50 percent against the British pound at $1.6818.
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 0.40 percent.
"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.
In a bid to boost the euro zone economy and avoid Japan-like deflation, the ECB cut interest rates to record lows, introduced fees in the form of negative interest rates on overnight depositors, and offered banks new long-term funds.
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, 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 and the Dow to all-time closing highs.
Based on the latest available data, the Dow Jones industrial average rose 98.58 points, or 0.59 percent, to 16,836.11; the S&P 500 gained 12.57 points, or 0.65 percent, to 1,940.45. The Nasdaq Composite added 44.59 points, or 1.05 percent, to 4,296.23.
Prices of U.S. Treasury securities fell on the ECB announcement but recovered, with benchmark 10-year notes last up 8/32 in price to yield 2.58 percent, the same as before the ECB decision.
"It probably puts pressure on U.S. rates to the extent that it's putting pressure on risk-free rates in Europe," said portfolio manager Chris Diaz 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)