PRECIOUS-Gold hits six-week peak on weak dollar, short-covering

* Dollar index at 13-month low

* Silver hits highest since June 29

* Palladium at strongest level since June 23

(Adds quotes, updates prices, changes dateline from BENGALURU) LONDON, July 27 (Reuters) - Gold touched its highest in six weeks on Thursday, lifted by short-covering and a weak dollar after investors bet U.S. interest rates could be kept low for longer. The U.S. Federal Reserve kept interest rates unchanged on Wednesday but appeared less confident about inflation picking up. The decline in the greenback is a boon for dollar-denominated gold since it makes the metal less expensive for investors paying in other currencies. "Gold has been benefiting a lot recently from the weaker U.S. dollar plus some short-covering on the futures market, where you've had record short positions," said analyst Carsten Menke at Julius Baer in Zurich. "The normalization of positioning will leave about a 4-5 percent upside from these levels based on history, which would be towards $1,300."

Spot gold had climbed 0.2 percent to $1,262.58 an

ounce by 1042 GMT after reaching $1,264.90, its highest since June 15.

U.S. gold futures for August delivery advanced 1

percent to $1,262.20 an ounce.

The dollar index , a measure of the greenback against

a basket of six major currencies, was at a 13-month low, while U.S. Treasury prices gained after the Fed's policy statement was perceived to be dovish. "Considering that the Fed sees the near-term risk of the economy is neutral, I don't think the market will expect a third rate hike in the foreseeable future or at least in this quarter," said Mark To, head of research at Hong Kong's Wing Fung Financial Group. Gold is sensitive to rising U.S. interest rates, as these increase the opportunity cost of holding non-yielding bullion, while boosting the greenback, in which it is priced. Spot gold may break resistance at $1,264 per ounce and rise further to the next resistance at $1,271, according to Reuters technical analyst Wang Tao.

Meanwhile, holdings at SPDR Gold Trust , the world's

largest gold-backed exchange-traded fund, fell 0.63 percent to 795.42 tonnes on Wednesday from 800.45 tonnes on Tuesday.

In other precious metals, silver rose 0.5 percent to

$16.71 per ounce. It earlier hit $16.77, its highest since June 29.

Platinum dropped 0.1 percent to $928.30 per ounce, while palladium gained 1.1 percent to $875.25 an ounce

after touching $878.50, the strongest since June 23.

(Additional reporting by Nithin Prasad and Arpan Varghese in Bengaluru; Editing by Dale Hudson)