The contract on Friday touched a high of $74.46, which was the highest since November 2014, rallying on concerns that USA sanctions against Iran would remove a substantial volume of crude oil from world markets at a time of rising global demand. But some key countries, including India and Turkey, have already said they will not do so.
The United States would work with allies on a case-by-case basis but Washington did not plan to offer exemptions from sanctions, Hook added.
In the face of the damage that did to U.S. The country exports more than 2 million barrels of oil.
"In this battle", he said, "any country that tries to take Iran's place on the oil market will be guilty of treason against Iran. and surely one day it will pay the price of this treason".
However, "sanctions alone won't cut it - we'll need to use all of our policy levers, and the help of our allies", he said. "They should be preparing now to go to zero".
Eshaq Jahangiri made the comments Sunday in a televised speech.
After Trump announced his withdrawal from the Iranian nuclear agreement, Hook said the American diplomatic teams from the State and Treasury are bringing with them a message of cooperation and coordination.
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The US "down to zero" plan rests heavily on banning India and China from buying from the Iranians, and while Indian companies have suggested they will dial it back, China remains in the nuclear deal and nearly certainly won't give in to US demands.
Delegations from State and Treasury departments have already visited 13 countries to co-ordinate the return of sanctions, and more than 50 worldwide firms have announced their intent to leave the Iranian sector since May, Mr Hook said.
"Member nations of the Organisation of Petroleum Exporting Countries (OPEC) and the leading non-OPEC oil producer Russian Federation, should maintain the Algiers Pact they forged in September 2016 so that oil prices will continue to ramp up", Sonatrach CEO Abdelmoumen Ould Kaddour said.
The collapsing economy has sparked new protests in Iran, with gunfire erupting Sunday morning as Iranian security forces confronted protesters demonstrating over water scarcity in the country's south.
There were also three days of demonstrations last week in Tehran, with groups confronting police outside parliament and rallies temporarily shutting down the city's Grand Bazaar, according to the AP.
"Our goal is to increase pressure on the Iranian regime by reducing to zero its revenue on crude-oil sales", Brian Hook, the State Department's director of policy planning, said at a briefing.
Oil prices rose strongly last week, with the U.S. crude contract hitting its highest in 3-1/2 years at $74.46.