Pompeo, who has voiced staunch opposition to Iran, said he sent the letter to Gen. Qassem Soleimani, a leader of Iran's Islamic Revolutionary Guard Corps and elite Quds Force, but the general didn't read it.
"I sent a note. I sent it because he had indicated that forces under his control might in fact threaten U.S. interests in Iraq," Pompeo said at a defense forum at the Ronald Reagan Presidential Foundation and Institute in Simi Valley, California. "He refused to open the letter - didn't break my heart to be honest with you."
"What we were communicating to him in that letter was that we will hold he and Iran accountable ... and we wanted to make sure that he and the leadership of Iran understood that in a way that was crystal clear."
Pompeo said Iran is working to strengthen its influence throughout the Middle East. As a Republican congressman from Kansas, Pompeo was highly critical of the Iran nuclear deal, which the U.S. and other nations negotiated with Tehran to lift sanctions in exchange for reductions in its nuclear program. Pompeo said Iran is currently in compliance with that agreement.
In Iran, Mohammad Mohammadi Golpaygani, the chief of staff for the country's supreme leader, said Soleimani ignored the letter. "Recently, when ... the CIA chief through one of his contacts in the region sent a letter to Gen. Soleimani, he responded by saying, 'I did not either receive or read the letter. I have nothing to tell these people'," Golpaygani said.
In a wide-ranging panel discussion, Pompeo would not answer questions about speculation that he could replace Rex Tillerson as secretary of state. Pompeo, an outspoken conservative, has a close relationship with President Donald Trump and personally delivers an intelligence briefing to the president nearly every day.
Pompeo declined to say whether he has had conversations with Trump about the possibility of replacing Tillerson, saying only that he was very focused on his job as CIA director.
On North Korea, Pompeo said U.S. intelligence on the progress of Pyongyang's nuclear missile program is good.
"I think we have a pretty good understanding of the scope and scale of their program and how far they are making progress towards being able to reliably deliver that system against the United States," Pompeo said.
He said U.S. intelligence agencies believe that North Korean leader Kim Jong Un does not have a good idea about how tenuous his situation is domestically and internationally.
"Those around him are not feeding him the truth about the place that he finds himself - how precarious his position is in the world today. It's probably not easy to tell Kim Jong Un bad news," he quipped.
Pompeo said the U.S. hopes that economic and diplomatic actions being leveled at North Korea, along with pressure from China, will resolve the nuclear threat "in a way that doesn't require the military outcome that I know no one is excited to advance."
Former CIA director Leon Panetta, who appeared with Pompeo, criticized Trump for his brazen tweets, particularly his decision late last month to retweet a string of inflammatory videos from a fringe British political group purporting to show violence being committed by Muslims. The tweets drew sharp condemnation from world leaders and civil rights groups.
He said the White House should have a disciplined message and that Trump should use Twitter to advance his policies.
"I know the president loves to tweet. Frankly, if I had my way, I'd take that tweeter and throw it out the window," said Panetta, who also served as White House chief of staff and secretary of defense. "It just raises a little bit of concern about stability."
Pompeo disagreed. He said Trump's tweets have actually helped the intelligence agencies.
"I have seen things the president has put on his Twitter account actually have a real-world impact on our capacity to understand what's going on in other places in the world," Pompeo said. "That is, our adversaries responded to those tweets in ways that were helpful to us to understand command and control issues, who is listening to what messages, how those messages are resonating around the world."
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