* Dollar index slides back to near 8-month low
* Silver rallies to highest since late October
* Silver at its most expensive vs gold in 3 months
* GRAPHIC-Gold/silver ratio: http://tmsnrt.rs/1qNdaSX (Updates prices, adds comment)
By Jan Harvey
LONDON, April 12 (Reuters) - Gold rose to three-week highs on Tuesday as the dollar sank back to a near 8-month low, weighed down by expectations that the Federal Reserve will keep U.S. interest rates lower for longer.
The U.S. currency has been on the back foot since Fed Chair Janet Yellen last month doused expectations for near-term hikes in U.S. interest rates, lifting dollar-priced assets, such as gold.
Spot gold XAU= touched a high of $1,262.60 an ounce before easing back to $1,258.26 by 1350 GMT, little changed from late on Monday. U.S. gold futures GCv1 for June delivery were up $2.60 an ounce at $1,260.60.
Silver XAG= also broke above $16 an ounce for the first time in nearly a month, peaking at a 5-1/2 month high of $16.19 before edging back to $16.07, up 1.2 percent. The metal rose 3.6 percent on Monday, its biggest one-day rise in over six months.
The bullion prices are being driven by the poor performance of the dollar and of stock markets, Afshin Nabavi, head of trading at MKS in Switzerland, said, with silver driving the market.
"Silver should get its head above $16.17 for sharp move higher," he said. "If silver continues, gold should break above $1,265 and eventually move towards $1,300."
The gold/silver ratio, which measures the number of silver ounces needed to buy an ounce of gold, hit its lowest in two months as silver outperformed gold. An ounce of gold now buys 78.2 ounces of silver, compared with 83.3 ounces in late February.
Speculation that interest rates will stay low also helped gold and silver in their own right. Rising rates lift the opportunity cost of holding non-yielding assets such as bullion.
Scaled-back expectations for further monetary tightening this year helped gold to its best quarter in nearly 30 years in the three months to March, after the U.S. central bank raised rates in December for the first time in nearly a decade.
"Negative yields in my opinion remain the key reason for buying gold, and silver. That story will not go away," Saxo Bank's head of commodities research Ole Hansen said.
"(Gold) found the expected resistance at $1,255 and it was only when silver took off that it managed to get through. Silver ETF holdings have risen strongly this past month while gold has been almost flat. That could indicate some switch in focus to silver, and the move yesterday highlighted that."
Among other precious metals, platinum XPT= was up 0.9 percent at $996.97 an ounce and palladium XPD= was up 0.3 percent at $546.66 an ounce.
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http://tmsnrt.rs/1qNdaSX
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