"We will work with them in any way we can, but they can't have a nuclear weapon," Trump said in a Cabinet meeting. "They can't be testing ballistic missiles."
Pompeo, who also attended the Cabinet meeting, echoed the sentiment, saying, "Iranians, for the first time, are saying they are willing to negotiate their missile program."
The headlines pushed U.S. crude down to the $57 per barrel level, while the global benchmark Brent is hovering around $64 per barrel.
Iran recently began surpassing uranium enrichment limits set in the 2015 nuclear deal but said these moves can be reversed if given enough economic incentives to offset U.S. sanctions.
The official website of Iranian President Hassan Rouhani on Sunday quoted him as saying, "The moment you stop sanctions and bullying, we are ready to negotiate."
Regional tensions have spiked a year after the Trump administration unilaterally withdrew from Iran's nuclear deal.
The U.S. has since re-imposed harsh sanctions on Tehran's oil exports, exacerbating an economic crisis that's sent its currency plummeting and pushed the country into a recession.
The Associated Press contributed to this report.