The U.S. dollar held firm against major peers on Tuesday, following its biggest rally in two weeks after strong services data in the United States fuelled bets the Federal Reserve may lift interest rates more than recently projected.

The Australian dollar languished near a one-week low ahead of a looming central bank rate decision, with market participants watching for signs of a pause in tightening after inflation unexpectedly cooled last month.

The U.S. dollar index - which measures the currency against six major peers - changed hands at 105.11 in early Asian trading, easing 0.1% after Monday's 0.7% rally, its biggest since Nov. 21.

It had dipped to 104.1 for the first time since June 28 as traders continued to rein in bets of aggressive Fed tightening.

However, it later reversed course as the Institute for Supply Management's (ISM) non-manufacturing PMI unexpectedly rose, indicating the services sector, which accounts for more than two-thirds of U.S. economic activity, remained resilient.

The Federal Open Market Committee decides policy on Dec. 15. Traders currently expect a half-point hike to a 4.25-4.5% policy band and a terminal rate of just above 5% in May.

"The dollar really kicked butt across the board," said Bart Wakabayashi, branch manager at State Street in Tokyo. "I think there was some positioning short dollars, and all the overnight economic releases from the U.S. were very strong and pointed to a hawkish Fed. They'll raise rates as long as the data shows they need to."

U.S. long-term Treasury yields climbed the most since Oct. 20 overnight, sending the yield-sensitive dollar-yen pair 1.83% to as high as 136.835. The dollar eased 0.25% on Tuesday though to 136.46 yen.

The euro rebounded 0.13% to $1.0505 following a 0.46% slide overnight. Sterling recovered 0.16% to $1.22035 after Monday's 0.88% retreat.

The Aussie dollar rose 0.21% to $0.6713, clawing back some of a 1.4% overnight tumble.

The Reserve Bank of Australia is universally tipped by economists in a Reuters survey to raise the key rate by a quarter point at 0130 GMT.

The bigger focus will be any clues in the policy statement on the outlook for the following meeting in February, after soft CPI data suggested a peak in inflation might be close.

In recent days though, RBA policy has taken a back seat to optimism about an easing of strangling COVID-19 restrictions in China, a top trading partner.

The Aussie reached a 2-1/2-month peak of $0.6851 on Monday, with sources telling Reuters a policy shift in Beijing around COVID could come as soon as Wednesday.

In terms of the RBA, "the risk sits with no change, but we consider this is a small risk," Carol Kong, a strategist at Commonwealth Bank of Australia, wrote in a client note.

"We expect the RBA to change its forward guidance in a subtle but significant way from 'expects to increase interest rates further' to 'likely to increase interest rates further' or 'willing to increase interest rates further,' (which) would indicate the RBA considers it is at or at least near the end of its tightening cycle," pushing the Aussie lower.

"But any RBA-induced losses in AUD may prove short-lived while markets remain optimistic about China exiting its strict COVID policies," Kong added.

(Reporting by Kevin Buckland; Editing by Sam Holmes)