TOKYO—The head of Japan’s Olympic organizing committee rejected the possibility of a long postponement of the Tokyo Summer Games, rebuffing a suggestion by a committee executive board member.

Yoshiro Mori, the president of the organizing committee and a former prime minister, called a news conference Wednesday to respond to a Wall Street Journal interview a day earlier with board member Haruyuki Takahashi, who said a delay of one to two years would be the most realistic option if the coronavirus epidemic made it impossible...