While Saudi Arabia has signaled that it will pump more oil, it has also indicated that OPEC and its oil market allies are not ready to lift price-boosting output caps . Led by Saudi Arabia, the producers have been trying to keep 1.2 million barrels per day off the market since January. They appear poised to continue limiting supply in the second half of 2019.

Supplies from Iran, one of the world's top oil producers, are expected to fall by hundreds of thousands of barrels per day in the coming weeks after Washington tightened sanctions on the Islamic Republic this month.

"We are confident that we've done the hard work to make sure that the market is well supplied, and I hope that we can continue to maintain that, and I think that we can," he told CNBC's "Squawk Box" on Thursday.

The administration has tried to assure Americans that U.S. allies in Saudi Arabia , the United Arab Emirates and elsewhere will fill the gap left by falling Iranian supply.

Secretary of State Mike Pompeo told CNBC on Thursday that the Trump administration has taken measures to prevent oil prices from spiking while it attempts to drive Iran's crude exports to zero.

Since President Donald Trump tightened sanctions on Iran, tensions have been rising in the Middle East.

The U.S. expedited the deployment of military assets to the Persian Gulf and withdrew diplomatic staff from Iraq, claiming threats by Iran against U.S. positions in the region. Meanwhile, Iran has ramped up production of nuclear materials, four vessels were sabotaged off the coast of UAE and Iran-aligned Houthi rebels in Yemen attacked oil infrastructure in Saudi Arabia.

Pompeo said the administration is not overhyping the threat from Iran, following reports that some members of the administration believe recent U.S. maneuvering in the region represents an overreaction to intelligence.

"We briefed Congress extensively on Tuesday," Pompeo said. "I think almost every member, Democrats and Republicans alike, walked out of that room understanding that the threats that we were discussing and the decision that President Trump made to take a posture to deter those threats and protect our forces were wholly justified and reasonable."

Despite the tension, Pompeo argued that the U.S. policy against Iran is not impacting oil prices much. He noted that Brent crude oil prices now at $69 a barrel are lower than a year ago, when the U.S. pulled out of the Iran nuclear deal and began restoring sanctions on the Iranian economy.

However, Brent prices rose to nearly four-year highs at $86.74 a barrel in October. Prices crashed in the final quarter of 2018, partly because Trump imposed looser oil sanctions on Iran than expected. Brent rallied nearly 40% to $75.60 last month and has since settled in a range between $69-$76 per barrel.

The view on Wall Street is that Middle East tensions, U.S. sanctions on Iran and Venezuela and uncertainty over whether OPEC will raise output are bolstering oil prices. The ongoing U.S.-China trade war is counteracting those bullish factors by raising concerns that global economic growth will falter and oil demand will sink.