* Dollar moves away from last week's 14-year highs
* "Hard Brexit" fears send sterling down sharply again
* Investors await Trump's news conference on Wednesday
* Graphic: World FX rates in 2016 tmsnrt.rs/2egbfVh
By Jemima Kelly
LONDON, Jan 10 (Reuters) - The dollar edged down for a second day on Tuesday, as cautious investors booked profits ahead of U.S. President-elect Donald Trump's first news conference since winning office, to be held on Wednesday.
Disquiet over whether Britain will undergo a "hard" exit from the European Union - in which immigration controls are prioritised over keeping access to the single market - continued to weigh on sterling, which hit a fresh 10-week trough against the dollar despite the latter's broader weakness.
The euro benefited, bouncing back over $1.06 to its highest levels so far this year, and strengthening to a two-month level of 87.635 pence against the pound.
"The market is increasingly nervous about Donald Trump's press conference - for FX markets what will be particularly important will be his plans ... for the trade policy, for the relationship with China," said Commerzbank currency strategist Esther Reichelt, in Frankfurt.
"The Fed has stressed this enormous uncertainty, so ... the main driver right now (for the dollar) is not monetary policy, because monetary policy will react to what we're going to hear from Donald Trump in the next couple of weeks."
The dollar index - which tracks the currency against a basket of six major peers - has climbed 4 percent since Trump's election on Nov. 8, as investors bet his promised programme of fiscal expansion will boost inflation and growth, and lead to a faster pace of interest rate rises.
On Tuesday, though, the index was down 0.2 percent at 101.77.
Boston Federal Reserve President Eric Rosengren on Monday called on the U.S. central bank to step up its pace of interest-rate increases from the once-a-year pattern it has pursued since 2015, warning of inflation risks if it does not.
At a separate event, Atlanta Fed President Dennis Lockhart said it was too early to judge how the incoming Trump administration may change the path of the economy.
Analysts said uncertainty over Brexit and over Trump's news conference were helping to spur a general risk-off tone across markets, which benefited the perceived safe-haven yen.
The dollar weakened as much as 0.6 percent to 115.365 yen as Tokyo traders returned to their desks after a public holiday on Monday, before recovering a touch to trade down 0.2 percent at 115.82 yen.
"Some Japanese customers are buying on dips with the dollar at the 115 level, but with Trump's speech ahead, some people are taking profits and adjusting their positions," said Kaneo Ogino, director at foreign exchange research firm Global-info Co in Tokyo.
For Reuters new Live Markets blog on European and UK stock markets see reuters://realtime/verb=Open/url=http://emea1.apps.cp.extranet.thomsonreuters.biz/cms/?pageId=livemarkets
Additional reporting by Tokyo markets team Editing by Jeremy Gaunt