Israel reiterated declarations it made in 1957 that any closure of the Straits would be considered an act of war. Nasser declared the Straits closed to Israeli shipping on May 2223. Jordan and Egypt signed a defense pact and the following day the Iraqi army began deploying troops and armored units in Jordan, later to be joined by Egyptian troops. On June 4, Israel responded with a large scale surprise air strike.
The question becomes, who started the war? Does a country like Israel wait until it is attacked when it see three countries amassing military units along it borders or strike first? In the ensuing conflict whereby Israel secured the area by the UNEF, should it now give it back.
Who moved first on that area?
you answered your own question, the naval blocake by Egypt started the war.