Following his comments, Iran said it had executed a man convicted of spying for the US.
Regional tensions have flared in recent days.
In response, the United States prepared to carry out a military strike against Iran but President Donald Trump said he had called it off at the last minute.
Major airlines from around the world on Friday began rerouting their flights to avoid areas around the Strait of Hormuz following Iran's shooting down of a us military surveillance drone there, as the USA warned commercial airliners could be mistakenly attacked.
Saudi Arabia says one person has been killed and seven others wounded in an attack by Yemeni rebels on an airport in the kingdom's south.
Hours after the incident, the United States military confirmed that one of its drones had been shot, claiming that the incident took place in worldwide airspace.
The attack comes less that two weeks after the airport in Abha was attacked by a Houthi cruise missile, wounding 26 passengers inside.
Pompeo also said "significant" sanctions on Iran would be announced on Monday aimed at further choking off resources that Tehran uses to fund its activities in the region.
"We're prepared to negotiate with no preconditions".
"Let us put politics aside and let us enjoy the company of our friends and, to some extent, our competition but that's OK", the president said.
A Pentagon spokeswoman, Commander Rebecca Rebarich, said on Saturday: "We stand by where we said the aircraft was operating in worldwide airspace".
"We are putting additional sanctions on Iran", Trump said.
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The data described in the executive order is different from hospital list prices made public earlier this year. The administration said that lack of transparency results in less competition and artificially high costs.
"I listen to everybody", Mr. Trump said.
On Thursday, Iran called the sanctions "economic terrorism".
"The signs show Iran is not seeking peace", Bolton said on Sunday, addressing media alongside Israeli Prime Minister Benjamin Netanyahu.
Iran eliminated some 97% of its enriched uranium to comply with the nuclear agreement with China, France, Germany, Russia, the United Kingdom and U.S. The country previously had enough material to build more than a dozen bombs. The Israeli leader appears to be wary of being seen as pushing the USA into a new Middle Eastern military conflict.
House Speaker Nancy Pelosi said no specific options for a US response were presented at the more than hour-long meeting. "I hope that happens, but it may not", Trump said.
Iran has said it would respond firmly to any threat against it and warned on June 23 of the risks of a military confrontation. It is not known whether the planned attacks on Iran will be carried out later, according to a source in The New York Times.
America's European allies have expressed deep concern about the volatile standoff.
"#EconomicTerrorism brings tension", Zarif Tweeted, adding it was "prudence" that prevented a war breaking out between Tehran and Washington.
"Everyone was saying I'm a war-monger, and now they say I'm a dove", Trump said on Saturday as he was peppered with questions about the Iran drama. While Iran has always said its program is civilian, world powers pursued the deal because they doubted that claim.
Limiting the volume and purity of its accumulated uranium was a central part of Iran's nuclear deal with world powers in 2015.
The US government on Saturday warned of possible Iranian cyber attacks.
Trump insisted it is up to the Iranian leadership how the current crisis plays out. His administration is aiming to cripple Iran's economy and force policy changes by re-imposing sanctions, including on Iranian oil exports. And I think they want to make a deal.
The regional tensions have prompted major worldwide carriers, including Saudi Arabia's state airline Saudia, to divert flight routes away from the Gulf of Oman and Strait of Hormuz.