Akbar Al Baker sees US president Donald Trump as a "friend of mine and of Qatar" but expects that there will "always be a little bit of friction".
The Qatar Airways chief executive's comments came weeks after the governments of the USA and Qatar signed an agreement that appeared to end a standoff over alleged state aid for airlines.
Asked about his appetite for further disagreements with Trump and the USA, Al Baker responded: "I'm a very small individual; I'm not a big bodybuilder, so I cannot have fights with presidents of other countries."
He adds: "There will always be misunderstandings between friends. But it doesn't mean that you walk away from your friendship. A friendship is always made for a long time."
Over the past three years, the US government had been pressured by American Airlines, Delta Air Lines and United Airlines, as well as their labour unions, to limit what they claim amounted to capacity-dumping by Qatar Airways, Emirates and Etihad Airways under open skies.
As part of the 30 January agreement, the Doha-based carrier must now use international accounting and auditing standards, disclose financial results and commit to not add fifth-freedom flights to the USA.
There are no indications that a similar agreement has been reached between the USA and the United Arab Emirates.
Al Baker was speaking at the launch of Air Italy in Milan.