Israel felt that Iran was the bigger danger to both Israel and the USA, and told the US so - that it would be more important to attack Iran. I remember reading the news reports at that time. Israel gave support to the invasion of Iraq but it was its second choice. In hindsight, Israel was right.
Yemeni Shiite rebels to form own Cabinet in 10 days (AP)
from the article: MI figures out what went wrong in Lavon affair - 55 years later