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FOREX-Dollar nurses losses after post-Fed sellof

* Fed raises rates, leaves rate outlook unchanged

* Core consumer price inflation slows

SINGAPORE, Dec 14 (Reuters) - The dollar nursed its losses in early Asian trade on Thursday, having tumbled after the Federal Reserve raised interest rates in a widely expected move, but left its rate outlook for the coming years unchanged.

The dollar index, which tracks the greenback against a basket of six major currencies, held steady at 93.444, after tumbling in the wake of the Fed's policy announcement and falling 0.7 percent on Wednesday.

The Fed raised key short-term rates by a quarter point to a range of 1.25-1.50 percent on Wednesday, as widely expected.

The Fed projected three more hikes in both 2018 and 2019 before a long-run level of 2.8 percent is reached. That is unchanged from the last round of forecasts in September.

Fed officials acknowledged in their latest forecasts that the economy had gained momentum in 2017 by raising their economic growth forecasts and lowering the expected unemployment rate for the coming years.

Traders and analysts said the dollar came under pressure after the Fed's policy announcement as the Fed kept its interest rate projections steady rather than revising them higher.

Some market participants had been speculating that the Fed could raise its interest rate projection for next year to four rate hikes, said Stephen Innes, head of trading in Asia-Pacific for Oanda in Singapore.

"From the market perspective, anybody who was leaning that way basically ran for the exit," Innes said, referring to the dollar's drop after the Fed meeting.

Against the yen, the dollar inched up 0.2 percent to 112.76 yen, after sliding 0.9 percent on Wednesday and having retreated from Tuesday's four-week high of 113.75 yen.

The euro edged up 0.1 percent to $1.1830, having climbed 0.7 percent on Wednesday.

The greenback had also weakened on Wednesday after U.S. core consumer price data showed slowing inflation, raising concerns the Fed will be less able to execute multiple rate increases next year.

Hopes for progress on U.S. tax reform, including tax cuts, is probably lending support to the dollar for now, said Teppei Ino, analyst for Bank of Tokyo-Mitsubishi UFJ in Singapore.

Against the yen, the dollar has support on the downside at its 200-day moving average which now lies at 111.65 yen, Ino added.

Congressional Republicans reached a deal on final tax legislation on Wednesday, clearing the way for final votes next week on a package that would slash the U.S. corporate tax rate to 21 percent and cut taxes for wealthy Americans. (Reporting by Masayuki Kitano; Editing by Eric Meijer)