June 9 (Reuters) - Gold prices were steady on Tuesday as traders assessed a fragile ceasefire between Israel and Iran, while awaiting any signs of progress in the wider Middle East conflict and focusing on concerns about inflation and rising interest rates.

Spot gold was steady at $4,332.50 an ounce by 0222 GMT. In the previous session, gold hit its lowest level in more than two months.

U.S. gold futures for August delivery fell 0.1 percent to $4,357.10.

Tim Waterr, chief market analyst at KCM Trade, said, "Gold trading is quiet as traders remain skeptical about the sustainability of the ceasefire between Iran and Israel and are cautious ahead of important US inflation data this week, which will help shape expectations for Federal Reserve policy."

Iran and Israel announced on Monday a halt to their exchange of attacks following an appeal from US President Donald Trump, but Tehran warned that it would resume hostilities if Israel continued to target Hezbollah in Lebanon.

Investors are preparing for the U.S. consumer price index data for May, due to be released on Wednesday, to assess the Federal Reserve's monetary policy path.

Silver fell 0.7 percent to $67.71 an ounce in spot trading, platinum dropped 0.2 percent to $1,751.39, while palladium rose 0.8 percent to $1,213.89.