He questioned whether Trump's words would do anything to reverse the effects on the market of declining Iranian oil production.
Saudi Arabia is said to have spare capacity of 2 million barrels per day, but it's not clear whether that much could be available immediately.
"Our goal is to increase pressure on the Iranian regime by reducing to zero its revenue from crude oil sales", Hook, the State Department's director of policy and planning, told reporters.
Abu Dhabi said it's ready to increase oil output in line with guidance set by OPEC and allied producers.
"We'll need more oil down the road and there'll be nowhere to get it", said Flynn, of the Price Futures Group.
Trump's suggestion means he wants Riyadh to increase production to 12 million bpd - something the kingdom has never done in the past.
The Trump administration has been counting on Saudi Arabia and other OPEC members to supply enough oil to offset the lost Iranian exports and prevent oil prices from rising sharply. China, the world's biggest oil consumer, and India, the country with the fastest-growing appetite for energy, added their own complaints after prices rose.
In a tweet on Saturday, Trump said Saudi Arabia had agreed to increase oil output by up to 2 million barrels, an assertion that the White House rowed back on in a subsequent statement.
"Further declines in US crude oil inventories and the significant outage in Libyan oil supply are helping to keep a floor under the market", said Harry Tchilinguirian, head of commodity markets strategy at BNP Paribas SA in London.
An agency report on Tuesday indicated, however, that despite the U.S. push on Saudi Arabia, futures in NY jumped as much as 1.7 per cent. But those moves may be tempered by an equal desire by the United States and other country for stable oil prices.
Multinationals that have halted business in Iran include oil companies of Total and Shell, the world's largest shipping container line Maersk, and aircraft producers of Airbus and Boeing.
On Tuesday a senior State Department official described tightening the noose on Tehran as "one of our top national security priorities".
"Oil is already being offered on the bourse, about 60,000 barrels per day, but that has been only for exports of oil products", Jahangiri said.
US President Donald Trump announced on June 30 that Saudi Arabia's King Salman had agreed to increase Saudi oil output by two million barrels per day to make up for the expected collapse in Iranian production.