The United States emphatically denied it.
Egypt was clearly embarrassed that the Jews could have been winning the war in such a dominating fashion, and this lie was to save face in the Arab world.
This backfired. Badly.
Two days later, Israel played a phone conversation between Egypt's President Nasser and Jordan's King Hussein where they hatched the story.
Israel played the message to the Arab world over and over aain:
Jordan, embarrassed, issued a statement admitting that it did not see any American or British planes:
This intelligence coup was also an embarrassment for the Soviet Union, which supplied the communications equipment to Egypt and Jordan that should not have been able to be intercepted. This leak seemed to also be designed to let America know that Israel is a valuable intelligence ally.
