The company said, however, that the weak Indian rupee continued to hit the rough diamond market and could upset forecasts.
The company reported first half sales unchanged from the previous year at $3.3bn, while its underlying operating profit contribution to majority owner Anglo American more than doubled to $571m, reflecting Anglo's increased stake in the diamond producer of 85%.
Prices of diamonds slumped after the 2008 financial crash and have still to fully recover, hurting the margins of and its main competitor, 's Alrosa.
"We are cautiously optimistic about world demand and clearly the US market is pulling well.
"The Chinese market is not bad," chief executive told reporters after the results were released on Friday.
"The world market grew by more than 2% last year and we are forecasting a growth for this year slightly higher than last year," he added.
Demand in the Gulf region was also strengthening, Mellier said, but local economic issues in weighed on forecasts.
"We are certainly more worried about the Indian market...we're more worried by the rupee and the liquidity problems in the country," Mellier said.
processes more than 90% of the world's diamonds, most of which are then exported to markets such as and the US.
The weakness of the rupee, down more than 7% this year against the dollar, could hit Indian demand for rough diamonds.
Mellier declined to give a diamond price outlook for the second half of the year, but said he expected a pick-up in market conditions in the fourth quarter to which "would react accordingly."