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LONDON, June 6 (Reuters) Hints from Federal Reserve chief Ben Bernanke that U.S. rates have further to rise sent Asian and European stock markets reeling on Tuesday, while bond yields rose and the dollar bounced off a one-year low against the euro.

Speaking on Monday, Bernanke said the U.S. central bank needed to remain vigilant on inflation even as the economy shifts to a slower pace of growth.

Investors interpreted Bernanke's comments as indicating the central bank would almost certainly raise rates again this month and the Nasdaq registered its biggest one-day percentage decline since January.

The prospect of a slowing U.S. economy and higher borrowing costs for American firms and consumers weighed heavily on Asian and European exporters, who rely heavily on U.S. demand for their products.

Japan's Nikkei fell 1.8 percent to its lowest close since January while Europe's FTSEurofirst 300 index slid more than 1 percent.

U.S. stock futures were pointing to a mild recovery on Tuesday.

''I think we went too far, and we were a little bit overextended yesterday,'' said Paul Mendelsohn, chief investment strategist at Windham Financial Services.

DOLLAR WINS RESPITE The prospect of the Fed raising rates for the 17th successive time to 5.25 percent this month sparked a round of dollar short-covering, helping the U.S. currency recover from a sell-off on a soft employment report late last week.

Futures markets are now showing a 75 percent likelihood of a rate hike at the Fed's two-day policy meeting that starts on June 28, up from less than 50 percent on Friday.

But the dollar's recovery was limited as some investors worried about the state of the world's biggest economy.

''Higher rates are a supportive factor for the dollar, but if the U.S. is raising rates due to inflation pressures, not growth, the impact on the dollar will be limited,'' said Tony Norfield, head of FX research at ABN AMRO.

The dollar, which hit a one-year low against the euro at $1.2980 on Monday, recovered to $1.2860, up a third of a percent on the day.

It rose a quarter-percent against the yen to 112.46.

The euro broke through 145.00 yen to a six-week high, finding support from expectations that a strong recovery warranted higher interest rates in the currency zone.

The European Central Bank meets on Thursday and is widely expected to raise rates by a quarter-point to 2.75 percent.

Signs of a strengthening recovery and rising price pressures, however, have raised speculation the bank could raise rates by as much as half a percentage point -- a move that would be its biggest hike in six years.

Data on Tuesday reinforced the recovery picture, showing the euro zone's service sector grew at its strongest pace in nearly six years last month.

OIL EASES Oil dipped, then steadied below $73 a barrel after Iran said world powers had made positive proposals to end a crisis over its nuclear programme, opening the door to more talks.

Oil swept to a record $75.35 in April as the dispute between Iran and the United States rumbled on. On Sunday, Iran's Supreme Leader Ayatollah Ali Khamenei said oil flows from the Gulf would be endangered if Washington made a ''wrong move''.

But there was a more conciliatory tone on Tuesday when Iran took delivery of a package of incentives put together by Britain, France and Germany then approved by the United States, China and Russia.

''The proposals had some positive steps in them and some ambiguities which should be removed,'' Ali Larijani, secretary of Iran's Supreme National Security Council, said after meeting European Union foreign policy chief Javier Solana.

U.S. crude oil dropped 48 cents to $72.42 a barrel immediately after the news, from $72.90 just before. By 1200 GMT it had steadied at $72.46 a barrel, down 14 cents on the previous day.

Gold slipped to $633.40 an ounce as the dollar recovered while base metals prices also eased.

Euro zone government bonds fell and U.S. Treasuries retained a weak tone. Benchmark 10-year Treasury notes were yielding 5.04 percent.

REUTERS MP GC1820