"We have 40 years of terror from this nation," Pompeo said on "This Week" Sunday, calling the incident, "one of the largest attacks on the global energy supply in history."
Defending President Donald Trump's strategy in dealing with the country, Pompeo said, "We are well on our way to forcing the Iranian regime to ultimately make the decision to become a normal nation."
On Friday, Secretary of Defense Mark Esper announced that Trump had approved a "modest deployment" of troops and air-and-missile defense systems to Saudi Arabia. The deployment will be, "defensive in nature," Esper said.
"It's about volume and density," Pompeo said in his interview with Raddatz on Sunday when asked whether the new defensive forces would make a difference. "It'll improve the capabilities for them."
"I don't think this type of posturing helps," Iranian Foreign Minister Javad Zarif said when asked about the deployment in a clip released ahead of an interview on CBS' "Face the Nation."
Also this past week, Trump announced sanctions on Iran's national bank, calling them "the highest sanctions ever imposed on a country."
"We're at the start of the sanctions campaign, not the middle or the end," Pompeo said. "The Iranian economy will shrink by somewhere on the order of 10 to 15% this year. And the regime knows their people won't stand for this."
While Houthi rebels have claimed responsibility for the attack, the secretary of state blamed it on Iran in a tweet shortly after the strike last weekend. He also called the Houthi claim false when speaking to reporters this week.
The Saudi government said Iran "sponsored" the attack during a news conference on Wednesday. Iran has denied responsibility for the attack.
"Our administration is taking this on in a serious way and we are working diligently to see that this has a diplomatic outcome," Pompeo said.
The United Nations General Assembly will be held this week, with leaders from around the world gathering in New York City. "We'll be at the U.N. all week talking about it," Pompeo said. "We hope the United Nations will take a strong position. It was designed exactly for this kind of thing, where one country attacks another country."
Also on "This Week," Pompeo was asked about recent reports that Trump asked the new Ukrainian president in a recent phone call to help investigate former Vice President Joe Biden, who is also a Democratic candidate for president.
"I do think if Vice President Biden behaved inappropriately, if he was protecting his son and intervened with the Ukrainian leadership in a way that was corrupt, I do think we need to get to the bottom of that," Pompeo said.
The Biden campaign has called for the release of the transcript from the telephone call between Trump and Ukraine's leader.
"We don't release transcripts very often," Pompeo said. "It's the rare case. Those are private conversations between world leaders and it wouldn't be appropriate to do so except in the most extreme circumstances. There's no evidence that that would be appropriate here at this point."