* Dollar holds most gains made vs euro after Fed
* Fed: no change on debt buying, deflation less of threat
* Dollar off peaks vs Swissie made on SNB intervention
* Aussie edges up vs dollar and yen
By Charlotte Cooper
TOKYO, June 25 (Reuters) - The dollar on Thursday held most of its gains made after the Federal Reserve signalled it was making no change to its steps to support the economy, but it began to lose its grip slightly as Asian share markets opened positively.
The Fed kept to its debt buyback programme and signalled it was less concerned about deflation, but it also said inflation would remain subdued for some time and interest rates would stay low for an extended period.
Its statement on Wednesday came after traders reported the Swiss National Bank was intervening in the market by selling the Swiss franc for dollars and euros, which sent the dollar up nearly 3 percent against the franc and lifted it across the board.
"The markets are still waiting for the dust to settle from the FOMC and the volatility seen overnight, not least of which seems from the SNB's very aggressive intervention," said Sue Trinh, senior currency strategist at RBC Capital Markets in Sydney.
"That saw the dollar rally very sharply and then of course we had the FOMC, and they didn't go out of their way to talk down rates, so that gave the U.S. dollar another leg up."
The euro fell 1 percent against the dollar on Wednesday.
It was creeping back in Asian trade on Thursday, gaining 0.2 percent to $1.3960, but was still well below Wednesday's pre-Fed high of $1.4139, when the market sold dollars on the view that the U.S. central bank would try to tamp down higher rate expectations.
The dollar index slipped 0.1 percent after climbing 0.7 percent on Wednesday, and the dollar edged 0.2 percent down to 1.0962 Swiss francs after a one-month high at 1.1026 on trading platform EBS on Wednesday.
Investors have been weighing up whether a rally in riskier assets such as shares and commodity-linked currencies should continue or whether it has got ahead of the economic recovery.
Tokyo's Nikkei share average rose 1 percent in early trade after falling sharply earlier in the week and as the Fed statement provided no surprises.
The Australian dollar rose 0.4 percent to $0.7999, although it was still below Wednesday's intraday high of $0.8056, and jumped 0.7 percent to 76.75 yen.
The euro also gained 0.5 percent to 133.93 yen as the Japanese currency weakened broadly.
Talk of Japanese investment fund outflows has been keeping a floor under yen crosses this week.
Four new Japanese investment trusts launched on Wednesday, all managed by Nomura Asset, attracted a combined 119.6 billion yen ($1.25 bln) in funds, according to data compiled by Reuters, and more are expected in before the end of the month. (Reporting by Charlotte Cooper and Satomi Noguchi; Editing by Hugh Lawson)