* Dollar index hovers near two-week highs
* Market unwinds dollar shorts after Fed announcement
* Fed keeps stimulus in place, not too alarmed on growth
By Jessica Mortimer
LONDON, Oct 31 (Reuters) - The dollar hovered near a two-week high on Thursday as some investors cut negative bets on the currency after the U.S. Federal Reserve kept its stimulus programme in place and its options for tapering its bond buying open.
In Wednesday's statement the U.S. central bank dropped a phrase expressing concern about a run-up in borrowing costs and made no direct reference to the partial government shutdown earlier this month.
The dollar index traded steady on the day at 79.759 but near a peak of 79.905 hit after the Fed announcement late on Wednesday, its strongest since Oct. 17. It has recovered from a nine-month low of 78.998 hit on Friday.
The euro lost 0.15 percent to $1.3713, pulling away from last week's peak of $1.3833. The euro stayed above chart support at $1.3651, the Oct. 21 low.
"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.
He still expected the Fed would not start scaling back monetary easing until March next year. This meant dollar gains would be limited, keeping the euro comfortably above $1.36.
Rasmussen saw scope for the euro to rise again in the short term, but said a breach of $1.40 was unlikely given some recent weaker euro zone data and concerns about the possibility of more monetary easing measures from the European Central Bank.
The single currency dipped after ECB governing council member Ewald Nowotny said earlier the central bank would provide more liquidity when cheap long-term loans it made in late 2011 and early 2012 expire.
Daisuke Karakama, market economist for Mizuho Bank in Tokyo, said the dollar could see more short covering in coming weeks.
"It is said that the year-end period, especially after mid-November, is when position-squaring tends to take place particularly among hedge funds and speculators."
The dollar fell 0.2 percent against the yen, however, to 98.26 yen, with weaker equity markets helping the safe-haven Japanese currency.
Bank of Japan Governor Haruhiko Kuroda on Thursday said Japan's economy was expected to grow above its potential and steadily follow a path towards the goal of 2 percent inflation.
However, three BOJ board members dissented against the latest semi-annual report, with some citing stronger downside risks to the economy.
The Australian dollar was up 0.25 percent at $0.9502 after surprisingly strong housing data suggested there may be less need for further monetary easing.
The New Zealand dollar was steady at $0.8262 after the Reserve Bank of New Zealand reiterated it was likely to hike interest rates next year.