Following the two sides' indirect discussions in Doha on Wednesday, US President Donald Trump, as well as mediators Qatar and Pakistan, offered signs that diplomacy was holding, despite exchanges of fire this week.
Cathay suspended flights to Dubai and Riyadh at the end of February after the war broke out.
The airline has raised fuel surcharges several times as the conflict has driven up oil prices.
It said Thursday it would resume daily passenger flights to Dubai and four-times weekly passenger flights to Riyadh from September 1.
Freighter services to Riyadh will resume from August 1.
"Cathay will continue to closely monitor the evolving situation in the Middle East prior to the resumption dates," the company said.