NEW YORK, Nov 3 (Reuters) - The dollar eased on Wednesday after the U.S. Federal Reserve said it would begin unwinding its pandemic-era stimulus, but held to its belief that high inflation would prove "transitory" and likely not require a rapid rise in interest rates. The Fed announced a $15 billion monthly cut to its $120 billion in monthly purchases of Treasuries and mortgage-backed securities, but did little to signal when it may begin the next phase of policy "normalization" by raising interest rates. The dollar index softened after the Fed statement, hitting a session low before reversing some of the losses and was last down 0.045% at 94.068, still within reach of its 2021 peak of 94.563 hit last month. The initial sell-off in the dollar after the Fed announcement was likely profit-taking, said Scott Petruska, chief currency strategist at Silicon Valley Bank. "The market was extremely long dollars going into this and they still are," he said. Over the rest of the quarter, the dollar will be supported by relatively higher U.S. yields, the Fed showing an eagerness to stop inflation and admitting to some extent that inflation may not be as transitory as they initially thought, and as a safe haven, he said. The Fed announcement follows meetings of the Reserve Bank of Australia on Tuesday and the European Central Bank last Wednesday, both of which pushed back against market pricing of tighter policy. The Bank of England meets on Thursday. read more ECB President Christine Lagarde said an interest rate rise in 2022 was very unlikely because inflation was too low, sending government bond yields lower. But the euro barely budged. read more Against the euro the greenback was nearly flat at $1.15825. That was not far from the $1.1522 low for the euro reached in October, which was the strongest level for the dollar since July 2020. Dollar/yen traded at 114.125, near a four-year high . The RBA on Tuesday abandoned its short-term yield target and dropped its expectation of holding rates at record lows until 2024, though the Aussie fell because the bank also pushed back on aggressive pricing for 2022 hikes. read more The Aussie dropped 1.2% against the dollar on Tuesday and sat at $0.7425 on Wednesday, down 0.05% from the session open. The New Zealand dollar was also dragged 1% lower on Tuesday, but found support on Wednesday from strong labor data and was up 0.27% at $0.71285. Money markets have dialled back expectations for a 15 basis point hike from the Bank of England on Thursday but still expect one before 2022. "The key question is how effective an interest rate hike will be in controlling inflation, mainly driven by supply chain issues, as we emerge from the pandemic," said Giles Coghlan, chief currency analyst at HYCM. The BoE is also focused on labor data and may decide to hold off on rate increases on Thursday, as "they will not want to hike rates too soon and risk crippling businesses’ recoveries," he said. Sterling recovered from a two-week low to trade 0.3% higher at $1.36525. Reporting by John McCrank in New York; Additional reporting by Tommy Wilkes in London; Editing by Andrea Ricci