* Euro touches 2-mth high of $1.3536 on EBS.
* Dlr falls on Fed decision to buy long-term Treasuries
* Plunge in US yields, better risk appetite weighs on dlr
* Euro hits three-month high vs yen
* Euro later sheds gains vs dollar and yen
By Masayuki Kitano
TOKYO, March 19 (Reuters) - The dollar hit a two-month low against the euro on Thursday, after the U.S. Federal Reserve engineered a sharp fall in U.S. bond yields by vastly expanding plans to buy assets, including government debt.
The Fed stunned markets on Wednesday by announcing it would buy $300 billion of long-dated Treasuries over the next six months, its first purchases of government debt since the early 1960s.
The euro jumped 3.9 percent against the dollar on Wednesday according to Reuters data, its biggest one-day percentage gain since the launch of the single European currency in 1999.
In early Asian trading on Thursday, the euro climbed to $1.3536 on trading platform EBS, the highest since early January. It later shed its gains and was down 0.2 percent from late U.S. trading on Wednesday at $1.3444.
"I think the dollar will continue to be sold across the board for the time being, over the next week or so," said Motonari Ogawa, a director at Barclays Bank in Tokyo.
The euro could heads toward $1.4000, helped by its yield advantage over the dollar, Ogawa said.
Benchmark 10-year Treasury note prices jumped four full points on Wednesday and their yields posted their biggest one-day drop since Oct. 20, 1987, the day after the 1987 stock market crash.
In addition to purchasing Treasury debt, the Fed said it would expand to $1.45 trillion an existing program to buy debt and securities issued by mortgage finance agencies.
It kept interest rates unchanged at a range between zero and 0.25 percent.
The sharp drop in U.S. bond yields, coupled with the fact that the Fed's steps may boost risk appetite by supporting the U.S. economy and equities, points to further dollar selling, said Yuichiro Nakamura, a trader for Shinkin Central Bank.
The dollar initially dipped against the yen, but later rebounded, rising 0.2 percent to 96.40 yen. The dollar fell nearly 3 percent against the yen on Wednesday.
The euro also climbed against the yen and hit a three-month high of 130.32 yen. It later shed its gains to stand at 129.60 yen, down 0.1 percent from late New York trade. (Additional reporting by Wayne Cole in SYDNEY and Shinji Kitamura in TOKYO; Editing by Chris Gallagher)