Sheikh Tamim bin Hamad Al Thani says: "I'm fearful that if anything happens, if any military act happens, this region will be in chaos."
Speaking to the American television network CBS's "60 Minutes" news programme, Sheikh Tamim also acknowledged that US President Donald Trump offered to host a meeting between the parties.
Sheikh Tamim said: "It was supposed to be very soon, this meeting. But I don't have any response."
The "60 Minutes" interview will air tonight in the US, Bahrain, Egypt, Saudi Arabia and the United Arab Emirates started boycotting Qatar in June over allegations it supports extremists, which Qatar denies.