Gold prices inched down on Friday, but were on track for their first weekly rise in three as a broadly weaker U.S. dollar and growing tensions in the Middle East lifted bullion's appeal.

Spot gold was down 0.2% at $2,020.7 per ounce, as of 0820 GMT, and has gained 0.4% so far in the week.

U.S. gold futures edged 0.1% higher to $2,031.6 per ounce. "There's a decent amount of physical buying, especially from the central banks, and the fact that the dollar has not really moved is also giving gold an element of support," Marex analyst Edward Meir said.

"Also helping on providing some support for gold are the geopolitical uncertainties and tensions."

Tension mounted in the Middle East as Yemen's Iran-aligned Houthis claimed responsibility for an attack on a UK-owned cargo ship, and they targeted Israel's port and resort city of Eilat with ballistic missiles and drones.

Meanwhile, the dollar index was heading for its first weekly dip in nearly two months, making the greenback-priced bullion less expensive to overseas buyers.

However, recent data showing higher-than-expected U.S. consumer and producer prices has dashed hopes for an early interest rate cut from the Federal Reserve and kept bullion's gains in check.

Fed policymakers should delay cuts by at least another couple of months to see if a recent uptick in inflation signals stalling progress toward price stability or is just a bump in the road, Fed Governor Christopher Waller said on Thursday.

Markets are currently pricing in a 62% chance of a Fed rate cut in June, according to the CME Fed Watch Tool. Lower interest rates boost the appeal of holding non-yielding bullion.

Spot platinum was down 0.1% at $900.80 per ounce and palladium fell 0.3% to $964.80. Silver lost 0.5% to $22.65 per ounce, but was down 3.2% so far in the week.

(Reporting by Sherin Elizabeth Varghese in Bengaluru; Editing by Subhranshu Sahu)