* Dollar supported after Fed's slightly hawkish stance
* U.S. data awaited for dollar to potentially consolidate gains
* Cross/yen demand helps underpin dollar/yen -trader (Updates prices, adds comments)
By Shinichi Saoshiro
TOKYO, Feb 1 (Reuters) - The dollar held steady against a basket of major currencies on Thursday after the Federal Reserve signalled its confidence about inflation and growth in the world's biggest economy, reinforcing views it will raise rates several more times this year.
Traders are now awaiting a host of indicators including non-farm payrolls to see if they offer more than a brief respite to the ailing dollar.
The Fed kept interest rates unchanged on Wednesday but said inflation is likely to quicken this year, bolstering expectations borrowing costs will continue to climb under incoming central bank chief Jerome Powell.
"The Fed's message was a little hawkish, but dollar reaction was limited as such a stance did not come as too much of a surprise," said Shin Kadota, senior strategist at Barclays in Tokyo.
"The heavy selling we saw on the dollar is beginning to run its course, but upbeat U.S. data would be needed for the currency to rebound further," Kadota said.
Upcoming U.S. data include Thursday's manufacturing ISM index and U.S. nonfarm payrolls and average hourly earnings due on Friday.
The dollar index against a basket of six major currencies was steady at 89.127 having crawled back from a three-year trough of 88.438 set last week. The index fell 3.2 percent in January.
The dollar edged up 0.2 percent to 109.36 yen, edging away from a four-month low of 108.280 plumbed on Friday.
It had lost 3.1 percent against the yen in January, weighed by a bevy of factors including concerns about U.S. trade protectionism and lingering speculation the Bank of Japan was gearing up to begin an exit from its easy monetary policy.
"Dollar/yen is still in a consolidation phase," said Tareck Horchani, head of Asia-Pacific sales trading for Saxo Markets in Singapore, adding that the dollar's bounce was still looking tepid.
Demand for cross/yen pairs, such as the Canadian dollar against the yen, is helping to weigh on the yen and supporting the U.S. dollar, Horchani said.
Some traders are trying to put bullish bets on the Canadian dollar against the yen, after data on Wednesday showed strong growth in Canada's economy in November, he added.
"The demand (for Canadian dollar) has been quite strong, even in the options market," Horchani said.
The Canadian dollar held steady at C$1.2312 per U.S. dollar, having set a four-month high of C$1.2250 on Wednesday.