* Major currencies mostly steady with no new leads
* U.S. markets closed for holiday last Friday
* ECB continues to sound dovish, may weigh on euro
By Ian Chua
SYDNEY, July 7 (Reuters) - The dollar clung on to most of last week's payrolls-inspired gains early on Monday after a holiday in the United States all but ensured a moribund start to the week.
The dollar index was steady at 80.300, not far from a one-week peak of 80.315 set on Thursday in the wake of solid jobs data. U.S. markets were shut on Friday for the Independence Day holiday.
"There are very limited leads for the region to work off this morning. Risk currencies have gotten off to a relatively flat start...which is a firm indicator that nothing much has changed sentiment-wise as of Friday," said Stan Shamu, strategist at IG in Melbourne.
The greenback kept almost all of last week's 0.7 percent gain on the yen. It was last at 102.11, near Thursday's peak of 102.27.
The euro, however, languished at one-week lows against the dollar and could stay under pressure after a top European Central Bank official underscored the need for interest rates to remain low for longer.
ECB policymaker Benoit Coeure, while urging euro zone governments to do their part to boost growth, said rates must stay very low for a long period of time to ensure monetary stability.
"One should expect a divergence of monetary conditions between the euro zone and the United States and Britain - where interest rates will at some point be lifted," he said on Sunday.
The euro traded at $1.3588, having fallen as far as $1.3585. The market could target $1.3575 initially, a level that had provided some support late last month.
Against the yen, the common currency was at 138.72 , down from last week's peak of 139.30.
Sterling remained a market darling and stayed within easy reach of a six-year high of $1.7180. The Canadian dollar, also in favour at the moment, traded at C$1.0653 per USD , just off a six-month high of C$1.0620 set Thursday.
The Australian dollar, in contrast, was still smarting from Reserve Bank of Australia Governor Glenn Stevens' remarks about it being overvalued.
The Aussie stood at $0.9355, nursing a 0.7 percent loss last week. Immediate support is seen at $0.9323, the 61.8 percent retracement level of its May 29-July 1 rally.
Investors in Asia looking for fresh inspiration will probably have to wait a little longer, given a dearth of major economic data due in the region.
In Europe, German industrial production figures and a euro zone sentiment report are due later in the day.
Key events this week include Chinese inflation data and minutes of the Federal Reserve's last policy meeting on Wednesday, the Bank of England's rate review on Thursday, and profit results and outlooks from major U.S. companies. The second quarter U.S. earnings season gets underway this week.