* Gold price highest since Jan. 5

* US producer prices unexpectedly fall in December

* US and Britain carry out strikes against Houthis in Yemen

Jan 12 (Reuters) - Gold prices rose more than 1% to a one-week high on Friday as an escalation in Middle East conflict fuelled safe-haven buying, and a softer U.S. producer price index data boosted bets that the Federal Reserve might cut rates sooner.

Spot gold was up 1.5% at $2,057.89 per ounce at 9:30 a.m. ET (1430 GMT), extending its run above the $2,000 level to nearly a month. U.S. gold futures gained 2.1% to $2,060.90

The United States and Britain launched strikes against sites linked to the Houthi movement in Yemen, while Saudi Arabia called for restraint.

A rise in geopolitical risk is pushing gold prices up, and at the same time the U.S. central bank may be getting ready to start moderating its restrictive monetary policy, also a good environment for gold, said Bart Melek, head of commodity strategies at TD Securities.

The PPI data came in negative, which was also a significant catalyst for prices, Melek added.

U.S. producer prices unexpectedly fell in December amid a decline in the cost of goods, while prices for services were unchanged, which bodes well for lower inflation in the months ahead. However, data on Thursday showed U.S. consumer prices rose more than expected in December.

Traders see an 80% probability of a rate cut in March, according to the CME Fedwatch tool, compared with about a 70% chance seen before the PPI report.

Considered a safe haven, gold tends to gain during times of uncertainty, while lower rates also lift the appeal of the zero-yield asset.

On the physical front, gold demand in most of the top Asian hubs firmed this week as the approaching Chinese New Year encouraged buyers in China and Singapore.

Spot silver rose 2.7% to $23.37 per ounce, platinum gained nearly 2% to $932.83, and palladium was up 0.8% to $995.89. (Reporting by Anushree Mukherjee in Bengaluru; Editing by Kevin Liffey)