SINGAPORE (Reuters) - The dollar hit its highest in a month on Thursday and pressed the euro towards major support levels, after the Federal Reserve set the stage for rate hikes next year -- far sooner than its developed market peers are expected to move.The U.S. central bank left policy settings unchanged overnight and, as expected, did not announce the beginning of asset purchase tapering. But the Federal Reserve said “a moderation in the pace of asset purchases may soon be warranted” and Fed Chair Jerome Powell said board members believed tapering could conclude around mid-2022, opening the way for rate hikes after that. The dollar rose broadly after his comments, especially against the euro and yen. The U.S. yield curve flattened and Fed funds futures markets moved to price a 50% chance of a hike in October and to fully price a 25 basis point rate hike in December. At a one-month low of $1.1684 in early Asia trade, the euro is close to its 2021 trough of $1.1664 and not far from major support at $1.1602, a break of which could open the way to falls as far as $1.14. Liquidity was lightened by a holiday in Japan on Thursday. “Powell didn’t give any specifics about the start of the taper, he said there was broad agreement in the end of taper, one which ‘concludes around the middle of next year,’” said John Briggs, strategist at NatWest Markets.“This is in our view more important than when the taper starts, as it starts the clock on when the next hike may occur.” The yen also lost ground after Powell’s news conference and ended up falling 0.5% for the session - its sharpest drop in more than three months - taking it to 109.87 per dollar, about the middle of a range it has kept since March. The dollar index hit a one-month high of 93.526. The Bank of Japan, which met on Wednesday, made no policy changes and is not seen lifting rates anytime soon while the European Central Bank is also lagging the Fed. Fed members’ new projections have hikes starting in 2022.The yen, a safe-haven asset, had also suffered a bit on Wednesday because developer China Evergrande offered the market some relief after its main unit said it agreed to settle a bond interest payment with some domestic creditors. It still has to settle $83.5 million in interest on an offshore bond due on Thursday. The Australian and New Zealand dollars gave up gains after Powell’s remarks and traded slightly lower in Asia, with the Aussie last down 0.1% at $0.7323, while the kiwi dipped below $0.70 to $0.6992. [AUD/] The Bank of England meets on Thursday, with traders expecting it to keep rates steady but wary of any hawkish surprises. Sterling is hovering just above big chart support at $1.3615. [GBP/] Norges Bank, meanwhile, is widely expected to deliver the first hike among G10 central banks on Thursday. The Norwegian Crown was steady in Asia at 8.669 per dollar.