Katz said that partnering with the U.S. was in Israel's strategic interests of countering Ira and boosting ties with Gulf countries.
"Iraq is seeking to reduce tension in our region through calm negotiations and the presence of Western forces in the region will increase tension".
Al-Hakim stressed Israel's participation in such a mission was unacceptable.
The United States has been trying to persuade its allies to form an global coalition with the declared aim of providing "security" for merchant shipping in the Strait of Hormuz - through which about a fifth of all oil consumed globally pass -and other strategic Middle Eastern shipping lanes. All the US' allies except for the United Kingdom have so far refused to join the coalition.
It is not clear if Israel has been asked to participate.
His shocking statement came after reports of Israel thing part in a US-led mission to secure Western vessels in the Strait of Hormuz.
On Thursday, Commander-in-Chief of the Revolutionary Guard Major General Hossein Salami warned that any new conflict in the region would be a major threat to Israel's existence, saying "a new war will put the Zionist regime under a full-scale threat".
"Whenever our commanders wish to, they are able to detain any ship, even if it is accompanied by American and British forces", Tangsiri told Hezollah-affiliated Al-Mayadeen television in Lebanon.
Tehran and Washington have been locked in a battle of nerves since US President Donald Trump withdrew from a landmark 2015 nuclear deal with Iran a year ago and reimposed sanctions.
The US and its Gulf allies have accused the Islamic Republic of the tanker attacks - allegation that Tehran denies. "But we are committed to upholding freedom of navigation and reassuring worldwide shipping, which this deployment on operations aims to do", said Andy Brown, the ship's commanding officer.
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