* Dollar index steady, clings to previous day's gains
* Euro loses steam as short-covering rally fades
* U.S.-euro zone yield differentials could weigh on euro -analyst
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 80.634, staying above a near two-week trough of 80.240 touched last Friday.
The greenback was firm 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 $1.3590, having lost about 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 had widened to about 37 basis points on Monday , the fattest since 2007.
Against the yen, the dollar remained in familiar territory and last fetched 102.49 yen, staying below a one-month high of 102.80 yen set last Wednesday.
(Editing by Shri Navaratnam)