Wright's comments came as an attack on two oil tankers off Iraq killed at least one person, and oil prices briefly soared past $100.

Since launching the war on Iran, US President Donald Trump has sought to calm the markets by offering US Navy escorts for oil tankers and reinsurance facilities for shipping companies -- but no escorts have so far taken place.

"It'll happen relatively soon, but it can't happen now. We're simply not ready," Wright told CNBC. "All of our military assets right now are focused on destroying Iran's offensive capabilities and the manufacturing industry that supplies their offensive capabilities."

He added that it was "quite likely" such escorts would be taking place by the end of the month.

As Iran launches a new wave of attacks against Gulf energy targets, the International Energy Agency said the war "is creating the largest supply disruption in the history of the global oil market".

US and Israeli strikes on Iranian targets -- including energy infrastructure -- have also disrupted supplies.

IEA member countries have agreed to unlock 400 million barrels of oil from their reserves -- their largest release ever.

The United States will be releasing 172 million barrels, Wright said, under a swap arrangement that would see 200 million barrels flow back to its Strategic Petroleum Reserve (SPR).

However the move was unable to overcome fears about the choking of energy supplies, with the Strait of Hormuz -- through which a fifth of global crude passes -- effectively shut down.

Wright said he had meetings at the Pentagon on Thursday to discuss possible US Navy escorts for tankers.