LONDON/TOKYO, Dec 6 (Reuters) - The U.S. dollar index held firm on Tuesday, following its biggest rally in two weeks after strong services data in the United States fueled expectations for higher interest rates from the Federal Reserve than recently projected.

The Australian dollar perked up from near one-week lows after the Reserve Bank of Australia (RBA) raised rates for the eighth time in as many months.

The U.S. dollar index, which measures the currency against six major peers, was at 105.24, steady after Monday's 0.7% rally, its biggest since Nov. 21.

It had dipped to 104.1 on Monday for the first time since June 28. It later reversed course after data showing U.S. services industry activity unexpectedly picked up in November, with employment rebounding.

"The longer the U.S. economy is robust the more doubts are probably going to increase as to whether the U.S. will actually face a recession next year and whether the U.S. central bank will actually cut its key rate at that stage," said You-Na Park-Heger, FX Analyst at Commerzbank.

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.

German industrial orders recovered more than expected in October, but that failed to strengthening the euro, flat on the day at $1.0500 after on Monday touching its highest level since late June.

The Western price cap on Russian seaborne crude, which came into force on Monday, may start to show its impact on the energy market soon, said Francesco Pesole, FX strategist at ING.

"When adding an expected drop in temperatures in Europe from this week, the risks of a new rally in energy prices are non-negligible, and the euro is highly exposed to such risks," he said.

The Aussie dollar rose 0.3% to $0.6718, clawing back some of a 1.4% tumble on Monday as the RBA said it was not on a preset course to tighten policy but that inflation was still high.

"Whilst the RBA have spoken of a pause publicly, we may not be as close to one as I originally thought," said Matt Simpson, a senior analyst at brokerage City Index in Brisbane.

In volatile Monday trading, the Aussie reached a 2-1/2-month peak of $0.6851.

(Reporting by Joice Alves and Kevin Buckland; Editing by Alexander Smith)