* Dollar index down slightly, well above last week's low
* Yen gains quarter percent vs euro, dollar
* U.S.-euro zone yield differentials could weigh on euro
(Updates with start of European trade, changes dateline, previous TOKYO)
LONDON, June 10 (Reuters) - The yen inched higher on Tuesday, reflecting modestly less upbeat sentiment on stock markets as Europe opened and a pause in dollar buying after a round of healthy gains a day earlier.
The dollar rose almost half a percent against the euro on Monday, drawing support from a rise in the premium given by short-term U.S. bond yields since the European Central Bank's easing of official interest rates last week.
The jury, however, remains out on whether those moves by the ECB and recent improvement in the U.S. economy are enough to weaken the euro more durably and end a period of low volatility brought on by universally low interest rates.
Traders say large volumes of expiring euro-dollar options around $1.3600 were likely to keep the market around that level for most of this week.
Hans Redeker, head of global foreign exchange strategy at U.S. bank Morgan Stanley in London, argued that U.S. retail sales numbers on Thursday would add to the more positive picture of U.S. growth and to both a stronger dollar and stronger yen.
"The next big thing is going to be higher volatility. That is going to lead to a stronger dollar, but also the yen outpacing the dollar," he said.
The dollar index stood at 80.59 , well above a near two-week trough of 80.240 touched last Friday and holding on to most of Monday's gains.
The U.S. currency was steady against the euro at $1.3598 , having pulled back from last week's low of $1.3677.
A strong U.S. jobs report last Friday, and hawkish comments from St. Louis Federal Reserve President James Bullard overnight underpinned the dollar.
Bullard, who is not a voter this year on monetary policy, said the falling U.S. unemployment rate, together with other encouraging economic data, could prompt him to move forward his view on when interest rates should be raised.
The euro is within sight of a four-month low of $1.3503 hit on Thursday after the ECB cut rates to record lows and took its deposit rate into negative territory for the first time.
The euro could face further downward pressure in the near term, hampered by a widening in interest rate differentials between the United States and the euro zone, said Masafumi Yamamoto, market strategist for Praevidentia Strategy in Tokyo.
"Interest rate differentials could be a driver for the euro versus the dollar as well as the euro against sterling," he said.
The yield spread between two-year U.S. Treasuries and two-year German Bunds has widened to levels above 36 basis points this week, , the most since 2007.
The yen was up a quarter of a percent against the dollar and euro, at 102.28 yen and 139.08 respectively.
A trader for a Japanese bank in Singapore noted talk earlier in the day of dollar-selling versus the yen by Japanese exporters. The market chatter follows the greenback's gains versus the yen over the past few weeks.
The Australian and New Zealand dollars were both a touch higher . The kiwi has drawn strength from expectations the New Zealand central bank will raise interest rates again this Thursday, although there are also expectations it may signal a slowing of any further moves.
"Yes, they are going to hike rates but that is all priced in now and we expect a modestly dovish statement," said Morgan Stanley's Redeker. "The gains this morning are temporary."
(Editing by Nigel Stephenson)