"We are ready to sit down with them", Pompeo told a joint news conference in Switzerland with Swiss Foreign Minister Ignazio Cassis, adding however that "the American effort to fundamentally reverse the malign activity of this Islamic Republic, this revolutionary force, is going to continue".
After pulling out of the worldwide nuclear deal, Trump subsequently reimposed US economic sanctions in an effort to end Iranian oil exports to the global market, a financial lifeline for the Islamic republic.
Pompeo made the remarks after meeting Dutch Foreign Minister Stef Blok, with whom he also discussed security threats relating to new 5G telecommunications networks.
He was speaking following official talks with the US Secretary of State, Mike Pompeo, on Sunday.
Cassis said Switzerland would be pleased to serve as an intermediary, but not a "mediator" between the United States and Iran.
But Pompeo also said the USA will continue its effort to "fundamentally reverse the malign activity of Iran".
Cassis also mentioned the importance of a multilateral cooperation within the United Nations.
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Pompeo himself a year ago laid out 12 draconian demands he said Iran would need to meet before reaching a "new deal" with the United States, essentially addressing every aspect of Iran's missile programme and what Washington calls its "malign influence" across the region.
He was reacting to comments made by Iranian President Hassan Rouhani on Saturday insisting that his country would not be "bullied" into talks with the United States, and that any dialogue between the two countries needed to be grounded in "respect". The two sides have both said they are willing to talk, but at the same time defense officials from the two adversaries stoked tensions by warning each other over military responses. "Switzerland, of course, wishes there is no escalation, no escalation to violence".
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He meanwhile preferred to remain discreet about efforts, largely led by Switzerland, to ensure the release of a handful of American citizens being held in Iran, stating only that the issue was a top priority for Trump, and that Washington is "working with all willing nations to assist us". But, he said the release of unjustly jailed Americans in Iran and elsewhere is a U.S. priority.
Despite the United States withdrawal, Iran has remained a party to the nuclear deal that involves the five permanent members of the UN Security Council, Germany and the European Union.
Some analysts believe Iran is acting to restore leverage it has lost since Trump withdrew from the 2015 nuclear deal and the USA reimposed sanctions that have hobbled Iran's economy.
Washington's European allies say the USA decision to abandon the agreement was a mistake, which strengthens Iranian hardliners at the expense of Rouhani, a pragmatist who won two landslide elections on promises to open Iran up to the world.
"Mr. Pompeo's emphasis on maintaining maximum pressure on Iran reflects the continuation of the same faulty behavior that must be corrected", the spokesman said, quoted in a ministry statement.