* Euro falls, dollar index hits 2-week high
* Euro zone inflation at four-year low, unemployment high
* Market unwinds dollar shorts after Fed announcement
* Fed keeps stimulus in place, not too alarmed on growth
LONDON, Oct 31 (Reuters) - The euro fell to a two-week low against the dollar on Thursday after a fall in inflation to its lowest in nearly four years increased speculation that the European Central Bank will ease monetary policy further.
Helped by the euro's falls, the dollar hit a two-week high against a basket of currencies.
The U.S. Federal Reserve sounded somewhat less alarmed about the pace of the economic upturn than some investors had expected after a meeting on Wednesday, prodding the dollar higher.
The euro lost 0.7 percent to $1.3638, its lowest since Oct. 17.
Euro zone flash annual HICP inflation fell to just 0.7 percent in October. This may raise concerns among euro zone policymakers about deflation risks and damage to the economy from a strong currency. Euro zone unemployment was at a record high 12.2 percent.
ECB governing council member Ewald Nowotny said earlier on Thursday the central bank would provide more liquidity when cheap long-term loans it made in late 2011 and early 2012 expire.
"We have had a nasty combination of a lack of inflationary pressures and record unemployment, and the market's interpretation is that the ECB may sit up and take notice," said Jeremy Stretch, head of currency strategy at CIBC.
"The downside risks for euro/dollar look evident and $1.36 is a near-term target."
The dollar index rose 0.25 percent to 79.984, its highest since Oct. 17, as it pulled away from a nine-month low of 78.998 hit on Friday.
The U.S. central bank dropped a phrase in its statement on Wednesday expressing concern about a run-up in borrowing costs and made no direct reference to the partial government shutdown earlier this month.
"The market was expecting a relatively dovish outcome from the Fed and that's why we've seen some profit-taking. People had become too bearish on the dollar and too bullish on euro/dollar," said Arne Lohmann Rasmussen, head of foreign exchange research at Danske Bank.
The dollar fell 0.3 percent against the yen, however, to 98.19 yen. Weaker equity markets helped the safe-haven Japanese currency even as three Bank of Japan board members dissented against the latest semi-annual report, with some citing stronger downside risks to the economy.
The Australian and New Zealand dollars also gained against their U.S. counterpart on strong Australian housing data and after the Reserve Bank of New Zealand reiterated it was likely to hike interest rates next year.