PRECIOUS-Gold set for third weekly gain as US rate outlook offsets dollar strength

* U.S. accuses Iran of breaching Hormuz promises

* Brent crude oil slides more than 11% this week

* Spot gold down about 10% since Middle East war began on Feb 28

* U.S. March CPI data due at 1230 GMT (Updates prices, as of 0532 GMT)

By Pablo Sinha

April 10 (Reuters) - Gold steadied on Friday as U.S.-Iran ceasefire uncertainty lingered, but the metal stayed on course for a third consecutive weekly climb as investors priced in earlier and deeper U.S. rate cuts, supporting non-yielding bullion.

Spot gold held its ground at $4,764.54 per ounce by 0532 GMT. The metal, however, has gained 1.8% so far this week.

U.S. gold futures for June delivery fell 0.6% to $4,787.80.

The dollar index strengthened, making greenback-priced bullion more expensive for holders of other currencies.

"There's a lack of clarity about the way that the ceasefire is evolving in the Middle East and what that means to energy markets... so we're in sort of a little bit of a holding pattern (with gold) going into the final session of the week," said Kyle Rodda, senior financial market analyst at Capital.com.

Spot gold has fallen about 10% since the U.S.-Israel conflict with Iran erupted on February 28, with elevated energy prices sparking inflation concerns and the prospect of higher U.S. interest rates.

The fragile two-week ceasefire between the U.S. and Iran showed further strain on Friday, as Washington accused Tehran of breaching promises on the Strait of Hormuz.

Brent crude, however, has slid more than 11% this week on optimism that the ceasefire could reopen the Strait of Hormuz, through which about 20% of the world's oil and liquefied natural gas passes.

"If things break down, (gold) could end up back in mid-$4,000's pretty quickly. But if the ceasefire holds and the peace deal starts to look more likely, then we could push through $5,000," Rodda added.

On the data front, the U.S. Personal Consumption Expenditures index, the Federal Reserve's preferred inflation gauge, advanced 2.8% in the 12 months through February, in line with estimates, and likely rose further in March.

Investors are now looking out for March's U.S. Consumer Price Index data, due later in the day, for further clues on Fed's monetary policy direction.

Markets are pricing in a 31% chance for a U.S. rate cut of at least 25 basis points at the Fed's December meeting, according to CME's FedWatch Tool, up from 20% in the prior session.

Among other metals, spot silver rose 1.3% to $76.03 per ounce, platinum lost 2% to $2,061.10, and palladium fell 0.2% to $1,553.92.

(Reporting by Pablo Sinha and Noel John in Bengaluru; Editing by Sherry Jacob-Phillips)