LONDON, Oct 5 (Reuters) - The U.S. dollar edged back toward a one-year high versus major peers on Tuesday ahead of a key payrolls report at the end of the week that could boost the case for the Federal Reserve to start tapering stimulus as soon as next month. The safe-haven greenback was also supported by an equity sell-off that spread from Wall Street to Asia. The risk-sensitive Australian dollar was among the biggest decliners, with the Reserve Bank of Australia reiterating it doesn"t expect to raise interest rates until 2024 after keeping policy steady, as expected. The U.S. dollar index , which measures the currency against six rivals, rose 0.13% to 93.957, moving back toward Thursday"s peak at 94.504, its highest since late September 2020.The index had rallied as much as 2.8% since Sept. 3 as traders rushed to price in tapering this year and possible rate rises for 2022. The dollar has also benefited from haven demand amid worries spanning the risk of global stagflation to the U.S. debt ceiling standoff. "The dollar started the week on the back foot yesterday, failing to rise on yet another equity sell-off, and suffering from the OPEC+ decision to stick to gradual supply hikes (400k barrels/day) which sent oil prices (and oil-sensitive currencies) higher," ING strategists said in a note. "As highlighted in yesterday’s FX Daily, we think markets will keep buying the dips in the dollar, and this is what appears to have happened overnight, as the greenback rebounded across the board." Friday"s non-farm payrolls data is expected to show continued improvement in the labour market, with a forecast for 488,000 jobs to have been added in September, according to a Reuters poll. Meanwhile, an index of Asia-Pacific equities (.MIAP00000PUS) skidded 0.92%, following a 1.3% tumble overnight for the S&P 500 (.SPX). The Aussie dropped 0.34% to $0.7263, retreating further from Monday"s four-day high of $0.73045. The New Zealand dollar declined 0.34% to $0.6939, also backing away from a four-day peak at $0.6981. The Reserve Bank of New Zealand decides policy on Wednesday, with markets priced for a quarter point rate hike. "The RBA’s firm on‑hold stance is a weight on AUD," Commonwealth Bank of Australia strategist Joseph Capurso wrote in a report. For the RBNZ, "with markets already pricing a rate hike cycle, the likelihood of material NZD upside is low," he said. The dollar gained 0.25% to 111.19 yen , while the euro slid 0.21% to $1.15965. Sterling traded flat at $1.3612. While the consensus view is for further gains for the greenback - with speculators pushing net long bets to the highest since March 2020 - TD Securities warns that headroom may be limited. "While the near-term USD bias leans higher, we"re wary about chasing the move at these levels," Mark McCormick, TD"s global head of FX strategy, wrote in a report. "There"s a lot of bad global news priced into the USD" already, and "the key for markets in the weeks ahead is to sort out the extent of the risk premium already priced in versus how these factors play out," McCormick said.