Pompeo said in the notices that he chose to waive the travel bans in U.S. foreign policy and national security interests.
"The United States and those countries will be responsible for any consequences", Iranian Foreign Ministry spokesman Abbas Mousavi said.
Zarif, the USA -educated architect of the 2015 nuclear deal who came under attack from anti-Western hardliners in Iran after Trump pulled out of the agreement a year ago, signaled Tehran would be resilient in the face of US sanctions.
Industry experts said Monday that the sanctions could potentially remove up to 1.2 million barrels of oil per day from global markets.
"I think maximum pressure should mean maximum pressure", Senator Ted Cruz told Mr Pompeo earlier this month at a Senate Foreign Relations Committee hearing during which he implored the administration to adopt the strictest possible interpretation of the sanctions.
"The Iranian regime can demonstrate its seriousness regarding consular issues, including Iranians who have been indicted or convicted of criminal violations of United States [sic] sanctions laws, by releasing innocent USA persons immediately", the spokesperson said.
US President Donald Trump may not want war, Iran's Foreign Minister Javad Zarif has said, but that won't stop the hawks in his administration and Israel from "luring" him into one, possibly with a false flag attack.
The US announced the sanctions in November but some countries got temporary waivers that allowed them to import Iranian oil.
"The woman in jail in Australia is facing due process, a proper legal procedure, and she is alleged to have committed a very serious crime", he told reporters in London.
Trump’s threat to go to court over impeachment defies ruling
And even those Democrats who support impeachment concede it would be a lengthy and politically risky process. Since the release of Mueller's findings, Democrats have been conflicted on what the next steps should be.
He described the B Team as including Israeli Prime Minister Benjamin Netanyahu and Trump's national security adviser John Bolton.
He added: "It is not a crisis yet, but it is a unsafe situation".
Iran's foreign minister on Wednesday proposed a prisoner swap for a British-Iranian mother detained in Tehran, saying the United States should drop charges against an Iranian woman it is seeking in Australia.
"Now we hear about Nazanin Zahari and her child, and I feel sorry for them and I've done my best to help", Zarif said.
"And I put this offer on the table publicly now: Exchange them", he said.
The cuts led by OPEC are in part a response to ballooning US crude production, now at a record 12.2 million bpd, making the United States the world's biggest producer. "Those who have designed the policies that are being pursued do not simply want a negotiated solution", Zarif said, insisting that "Iran is not seeking confrontation, but will not escape defending itself".
"Let's have an exchange", Zarif said.
He went on to offer prisoner swaps with Washington.