Not willingly. Both superpowers had vested interests in the outcome of the war. Each country (Britain, France, Israel, The soviet Union and the United States) had different motives for doing what they did.
Britain and France had 2 motives: Oil and the Canal itself. Shipping was a huge consideration in the war.
The United States: mostly it was a matter of not letting the Arab nations get too upset. Oil again.
The Soviet Union: Oil and they were backing Egypt. The oil consideration was not for themselves. They (have/had) plenty of oil. They didn't want the balance of power shifting to the United States.
Israel: self preservation. That is always their motive.
