TOKYO, Sept 3 (Reuters) - Japan Display Inc Chief Executive Mitsuru Homma on Thursday said the screen maker's "biggest client", widely understood to refer to Apple Inc , is increasing orders ahead of the expected launch of a new iPhone this month.

Homma said weakness in China's smartphone market, the world's biggest, amid that country's broader economic slowdown did not appear to be affecting Apple's screen orders.

"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 Chief Executive Tim Cook last week reassured shareholders about the strength of the Chinese market for iPhones after a slump in China's stock market and the devaluation of the yuan rattled investors.

"I continue to believe China represents an unprecedented opportunity over the long term," Cook wrote in remarks that sparked a rebound in the U.S. giant's share price from a China-induced slump of 19 percent from its record high in February.

iPhone activations in China had accelerated over the past few weeks and the App Store in China had recently posted its best performance of the year, Cook said.

Japan Display was formed in a government-backed deal in 2012 from the ailing display units of Sony Corp, Toshiba Corp and Hitachi Ltd.

It initially struggled against Sharp Corp and other Asian rivals but it has been recovering due to strong Apple orders.

(Reporting by Ritsuko Ando and Reiji Murai; Editing by Stephen Coates)