SINGAPORE, Feb 6 (Reuters) - The U.S. dollar wobbled near a three-month peak as expectations the Federal Reserve is unlikely to cut rates aggressively this year take hold, while the Australian dollar rose after the central bank said it could not rule out another rate hike.

The Reserve Bank of Australia (RBA) on Tuesday left rates unchanged at a 12-year high of 4.35%, as expected, after its February meeting, but cautioned that a further increase in interest rates might be needed to tame inflation.

Investors have steadily moved to push back bets for the first rate cut from the RBA to August, rather than June, with economists polled by Reuters also expecting the central bank to stay steady on rates well into the second half of this year.

The Aussie rose 0.44% to $0.65115 after the decision, inching away from the 2-1/2 month low of $0.6469 it touched on Monday. The New Zealand dollar was 0.23% higher at $0.6069.

"It totally makes sense for the RBA to retain hawkish bias, given the pushback to easing expectations we have seen lately from the Fed, ECB and other major central banks," said Charu Chanana, head of currency strategy at Saxo in Singapore. "Bearish AUD picture remains intact, given the lags in RBA pricing compared to that of the Fed, as well as the broader downbeat China picture."

Meanwhile, the dollar index, which measures the U.S. currency against six rivals, eased a bit to 104.32, having touched 104.60 on Monday, its highest since Nov. 14. The index is up 3% for the year so far after dropping 2% in 2023.

Data on Monday showed U.S. services sector growth picked up in January as new orders increased and employment rebounded, indicating a strong start to the year for the economy. The data followed a blowout jobs report last week.

The string of robust U.S. economic data has quashed any lingering hopes of early and steep interest rate cuts by the Fed, with Fed Chair Jerome Powell and other policymakers also pushing back against the notion.

Traders have been scaling back rate cuts bets since the beginning of the year and are currently pricing in only a 16% chance of a cut in March, the CME FedWatch tool showed, compared with a 69% chance at the start of the year.

They are also now pricing in 115 basis points (bps) of cuts this year, compared with around 150 bps of easing anticipated in early January.

"There may still be a bit of room to scale back (more) but it's likely limited given that the disinflation trend in the US is becoming more entrenched and that labour market tightness is gradually easing," said Christopher Wong, a currency strategist at OCBC in Singapore.

In other currencies, the euro was little changed at $1.0750, while sterling last fetched $1.25495, up 0.11% on the day but remained close to the seven-week low it hit on Monday.

The pound's fall on Monday came despite some upbeat economic data. Figures showed that the unemployment rate was likely much lower late last year than previously thought, which could push out British rate cuts too.

"The tighter than expected UK labour market supports our view that interest rate cuts are still some way off," said Kristina Clifton, FX strategist and economist at Commonwealth Bank of Australia in a note.

"We expect the first cut in August versus current market pricing for the June cut."

The Japanese yen was stronger on the day at 148.44 per dollar, but not far off a two-month low of 148.90 it touched on Monday.

Japan's real wages fell for a 21st straight month though at a slower pace, while household spending dropped for a 10th consecutive month, showing inflation outpaced wage recovery and continued to weigh on consumer spending.

(Reporting by Ankur Banerjee in Singapore; Editing by Sonali Paul and Jamie Freed)