oil market will be guilty of treason against Iran. and surely one day it will pay the price of this treason", he said.
He said in the Fox interview that European companies would face sanctions if they traded with Iran now.
The State Department has insisted on multiple occasions that Giuliani does not speak on behalf of the administration on foreign policy issues.
After the remarks, USA crude jumped more than 8 percent and closed at more than $74 a barrel - a first since November 2014.
The United States exited from the nuclear deal between Iran and world powers in May and said it would reimpose economic sanctions on the Islamic republic and its business partners by 4 November.
Donald Trump is urging oil producing countries except Iran to boost output.
Since President Donald Trump withdrew the US from the Iran deal, his administration has been pushing for allies to stop importing Iranian oil before sanctions snap back into place in November.
Oil prices rose strongly last week, with the United States crude contract hitting its highest in 3-1/2 years at $74.46.
But Saudi Arabia, OPEC's biggest producer, was keen to raise output to meet calls from Trump and major consumers such as India and China to help cool oil prices and avoid shortages, according to Saudi officials including Energy Minister Khalid al-Falih.
In particular, the administration points to a recent announcement by Saudi Arabia to increase oil production, with President Trump tweeting Saturday that the country's leader King Salman agreed to increase oil production by 2 million barrels. "Prices to high! He has agreed!" The White House later walked back the comments. "Absolutely", the president responded when asked if the USA would sanction European countries that do business with Iran.
Hook said Monday the U.S.is "working to minimize disruptions to the global market, but we are confident that there is sufficient global spare oil production capacity".