* Dollar hits month low as Fed move seen as dovish
* Wall Street little changed after big post-Fed gains
* Sterling jumps after BoE rate-setter votes for hike
* Euro gains as Dutch election soothes EU breakup fears (Updates with open of U.S. markets, changes byline, dateline from London)
By Lewis Krauskopf
NEW YORK, March 16 (Reuters) - A key index of world stocks climbed to record highs while the U.S. dollar sank to a month low on Thursday as investors digested the recent U.S. interest rate increase and indications there would be no pick-up in the pace of monetary tightening.
European stock markets gained after the Dutch election victory by Prime Minister Mark Rutte which fought off a challenge by anti-immigration, anti-European Union rival Geert Wilders.
On Wall Street, major U.S. equity indexes were modestly lower in late morning trading after gaining sharply in the wake of the U.S. Federal Reserve's rate decision on Wednesday.
Fed Chair Janet Yellen pointed to growing faith in the economy's trajectory as the U.S. central bank raised rates for the second time in three months.
"Certainly, the Fed was dovish in their approach," said Bruce Bittles, chief investment strategist at Robert W. Baird in Sarasota, Florida. "The fact that the Fed raised rates, but not aggressively, but yet indicated that she had confidence in the economy certainly was a big help."
MSCI's all-country world stock index gained 0.7 percent, and hit an all-time high.
The Dow Jones Industrial Average fell 42.26 points, or 0.2 percent, to 20,907.84, the S&P 500 lost 6.12 points, or 0.26 percent, to 2,379.14 and the Nasdaq Composite dropped 8.82 points, or 0.15 percent, to 5,891.23.
The pan-European STOXX 600 index rose 0.6 percent and touched its highest level since December 2015, helped by the Fed's dovish tone and the Dutch election results.
Amsterdam's AEX index rose 0.5 percent and hit its highest in more than nine years.
"Some of that fear around Brexit, Trump, and then Wilders and (France's) Le Pen, may now be seeping out of the markets - you see some of that fear dissipating," said Arne Petimezas, analyst at AFS Group in Amsterdam, referring to far-right French presidential Marine Le Pen.
The dollar fell 0.3 percent against a basket of key currencies, adding to Wednesday's steep slide after the Fed's decision and touching a one-month low.
The euro edged up against the dollar, also buoyed by the Dutch election, after a big jump on Wednesday.
Sterling jumped after outgoing Bank of England policymaker Kristen Forbes unexpectedly voted for a rise in interest rates at the bank's March meeting.
U.S. Treasury yields rose from more than one-week lows on the view that they had fallen too sharply in the prior session after the Fed maintained its outlook for only a gradual pace of interest rate increases this year.
Prices on benchmark 10-year Treasuries US10YT-RR fell 6/32 to yield 2.524 percent, from 2.504 percent late on Wednesday.
Oil prices eased as support from a weaker dollar was offset by a stubbornly high level of U.S. inventories.
Brent crude was 6 cents lower at $51.75 a barrel. U.S. light crude was down 16 cents at $48.07 a barrel.
Additional reporting by Jemima Kelly in London; Editing by Bernadette Baum