Pompeo said Kerry's meetings with Iranian Foreign Minister Javad Zarif were "beyond inappropriate" and undermined U.S. foreign policy. Kerry has said he's met with Zarif a few times since leaving office in 2017.
President Donald Trump's administration has made its tough position on Iran a hallmark of its foreign policy agenda. In May, Trump decided to withdraw the U.S. from the Obama-era Joint Comprehensive Plan of Action, which included a pledge from Iran to abandon its stockpile of medium-enriched uranium.
Earlier this week, Trump tweeted that Kerry's meetings with Zarif were illegal.
"What Secretary Kerry has done is unseemly and unprecedented," Pompeo said Friday during a news conference. "This is a former secretary of state engaged with the largest state sponsor of terror."
Kerry dismissed the criticisms and said he had briefed Pompeo and the State Department about the discussions with Zarif and said Trump should "be more worried about Paul Manafort meeting with Robert Mueller than me meeting with Iran's [foreign minister]."
Kerry spokesman Matthew Summers told Politico the former secretary of state "stays in touch with his former counterparts around the world just like every previous secretary of state, and in a long phone conversation with Secretary Pompeo earlier this year he went into great detail about what he had learned about the Iranian's view."
"No secrets were kept from this administration," Summers said.
Kerry said he has talked with Zarif about the JCPOA nuclear deal.
During a Fox News interview this week, Kerry implied he encouraged the Iranian government to wait it out until there is a Democratic president again.
"I think everybody in the world is talking about waiting out President Trump," Kerry said.