Mitsuru Homma, who was appointed CEO in June, said weakness in China's smartphone market, the world's biggest, amid that country's broader economic slowdown was not affecting the orders for display screens it was getting from its top client.
"They're coming to us with more orders, saying 'give us more, give us more'. They keep increasing," he told Reuters in an interview.
Apple is expected to unveil the new iPhone at an event on Sept. 9. Some analysts have raised concerns that the planned introduction of a new feature called Force Touch, which distinguishes between light taps and presses, could cause production hiccups.
Asked about the new iPhone, Homma said: "There's difficult technology being used... But I think ramp-up is going well."
Japan Display shares rose as much as 5.5 percent on Thursday after Homma's comments before finishing up 3.8 percent at JPY 379. The benchmark Nikkei 225 average index rose 0.5 percent.
Apple Chief Executive Tim Cook last week reassured shareholders about the strength of the Chinese market for iPhones after a slump inChina's stock market and the devaluation of the yuan rattled investors.
It is unclear whether strong orders from Apple mean the US company is more bullish about the prospects of its new iPhone than previous models, or whether it is placing more orders with Japan Display at the expense of other suppliers. Japan Display does not reveal the total size of its business with Apple.
Some analysts see Japan Display's dependence on Apple as a concern, particularly given a slowing Chinese market.
"Although the strong relationship with Apple... is certainly positive, Apple's specifications are also quite high and we estimate profitability is lower than on other Japan Display products," Credit Suisse analyst Mika Nishimura said in a report on Thursday.
It initially struggled against Sharp Corp and other Asian rivals but it has been recovering due to strong Apple orders. In contrast, Sharpsought a $1.9 billion (roughly Rs. 12,586 crores) bailout in May due to its shrinking display business.
Investors have speculated that Japan Display could merge with Sharp's display business to create a more stable display maker, since both cater to high-end smartphone makers.
Sources have said Sharp was considering selling a stake in its display business to state-controlled fund Innovation Network Corporation of Japan, which is Japan Display's top shareholder. The fund could broker a merger, they say.
Homma said the company was not currently considering a merger with Sharp, although he did not rule out a future deal.
"We're currently in the midst of various restructuring measures. We don't have the capacity to consider such a move, and we haven't been asked to do so by our major shareholder either," he said.
"I think there might be reasons such discussions haven't come my way. But when such talks come, it will probably come suddenly."
© Thomson Reuters 2015