* Dollar index little changed, but holds well above last week's low
* Euro loses steam as short-covering rally fades
* U.S.-euro zone yield differentials could weigh on euro -analyst
(Updates prices, adds comments)
TOKYO, June 10 (Reuters) - The dollar held steady versus a basket of major currencies on Tuesday, clinging to gains made the previous day thanks to higher U.S. bond yields after last week's solid U.S. jobs report.
The dollar index stood at 80.607 , keeping above a near two-week trough of 80.240 touched last Friday.
The greenback held its ground against the euro, which pulled back from last week's high of $1.3677 as a short-covering rally following the European Central Bank's easing steps lost momentum.
The common currency was steady at $1.3591, after having lost 0.4 percent on Monday.
A strong U.S. jobs report on Friday, and hawkish comments from St. Louis Federal Reserve bank 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 retreat in the euro brought it back closer to a four-month low of $1.3503 touched on Thursday on trading platform EBS, shortly after the ECB cut interest 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," Yamamoto said.
According to Thomson Reuters data, the yield spread between two-year U.S. Treasury yields and two-year German government bond yields has widened to levels above 36 basis points this week, , the fattest since 2007.
Against sterling, the euro eased 0.1 percent to about 80.84 pence, not very far from an 18-month low of 80.64 pence set last Thursday.
Against the yen, the dollar eased 0.1 percent to 102.39 yen , down from a one-month high of 102.80 yen touched on June 4.
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.
A rise in the benchmark 10-year U.S. Treasury yield from an 11-month low of 2.042 percent set in late May has helped bolster the greenback's appeal. The 10-year U.S. Treasury yield last stood near 2.60 percent.
Meanwhile, the yen has been pressured recently by gains in Japan's Nikkei share average, which touched a three-month high earlier this week
Gains in Tokyo equities is seen as negative for the yen, since sustained rises in stocks could bolster Japanese investors' risk tolerance and whet their appetite for overseas assets over the medium term.
(Editing by Shri Navaratnam)