(Corrects sterling milestone to three-year high, not three-month high) * Graphic: World FX rates https://tmsnrt.rs/2RBWI5E By Kevin Buckland TOKYO, June 1 (Reuters) - The dollar languished near multi-month lows versus major peers on Tuesday, as traders pondered the prospects for early policy normalisation by the Federal Reserve ahead of a key jobs report at the end of the week. The British pound rallied to a three-year peak at $1.425, while Canada's loonie hovered near a six-year top, amid market expectations for policy tightening in those countries. Australia's dollar rose for a second day to as high as $0.77605, ahead of a central bank announcement at 0430 GMT, although economists predict no change to monetary policy. The offshore Chinese yuan edged back toward Monday's three-year high of 6.3526 per dollar, last trading at 6.3640, paring a retreat spurred by the monetary authority's tightening of banks' FX requirements to stem the currency's rise. The dollar index, which tracks the greenback against six peers, was back below 90 from as high as 90.447 on Friday, when a measure of U.S. inflation closely watched by the Fed posted its biggest annual rise since 1992. The gauge sank 0.3% on Monday, in a market thinned by U.S. and British holidays. Fed officials, led by Chair Jerome Powell, have said repeatedly they expect price pressures to be transitory and monetary stimulus to stay in place for some time, but investors are wary that a strong pandemic recovery could force the Fed's hand. Vice Chair Randal Quarles and Governor Lael Brainard will both be speaking at separate events on Tuesday, while nonfarm payrolls numbers on Friday will be even more closely scrutinized than usual after the much-weaker-than-expected reading a month ago. Commonwealth Bank of Australia strategist Joseph Capurso says that trimmed measures of inflation, which eliminate the most extreme price changes, show the U.S. has no inflation problem, and markets will need to unwind some of the expectation for near-term policy tightening, which will weigh on the dollar. The global pandemic recovery will provide an additional headwind, he said. "The world economy is clearly recovering, and that is going to be bad for the U.S. dollar because it’s a counter-cyclical currency," Capurso said. "The U.S. dollar has been pretty heavy in the last few weeks, and I think it keeps trending lower." That includes a drop to $1.24 per euro by the end of this month, extending to $1.32 by the middle of next year. The euro gained 0.1% to $1.22325 on Tuesday, not far from a nearly five-month high of $1.2266 touched last week. The dollar fell for a second day against the yen, weakening 0.2% to 109.375. The pair had climbed as high as 110.20 on Friday, following the inflation data. ======================================================== Currency bid prices at 139 GMT Description RIC Last U.S. Close Pct Change YTD Pct High Bid Low Bid Previous Change Session Euro/Dollar $1.2233 $1.2225 +0.07% +0.13% +1.2236 +1.2224 Dollar/Yen 109.3450 109.4600 -0.02% +5.95% +109.5520 +109.4400 Euro/Yen Dollar/Swiss 0.8983 0.8987 -0.04% +1.54% +0.8987 +0.8981 Sterling/Dollar 1.4243 1.4215 +0.20% +4.25% +1.4248 +1.4209 Dollar/Canadian 1.2048 1.2071 -0.19% -5.38% +1.2065 +1.2047 Aussie/Dollar 0.7761 0.7728 +0.45% +0.92% +0.7762 +0.7736 NZ 0.7282 0.7275 +0.12% +1.43% +0.7283 +0.7270 Dollar/Dollar All spots Tokyo spots Europe spots Volatilities Tokyo Forex market info from BOJ (Reporting by Kevin Buckland)