NEW YORK – Secretary of State Mike Pompeo on Sunday accused Iranian leaders of being "bloodthirsty" and eager for war and suggested President Donald Trump would take additional steps to retaliate against Tehran for its alleged role in attacks on Saudi Arabia's oil facilities.

“This was an attack by Iran on the world," Pompeo asserted in an interview with CBS' Face the Nation.

"We’re looking for a diplomatic resolution to this, unlike the Iranians," Pompeo said, as he and other diplomats gathered in New York for high-level meetings at the United Nations General Assembly. "… Apparently the Iranians are bloodthirsty and looking for war."

Pompeo's red-hot rhetoric seemed out of sync with Trump's own stance on the Sept. 14 attack, which temporarily slashed Saudi Arabia's oil-producing capacity. Unlike Pompeo, Trump has so far declined to directly accuse Iran of being behind the strikes. And Trump has not likened the incident to an act of war.

Trump has said he does not want war with Iran, and so far, he has opted for a cautious, limited response. He announced new sanctions on Iran's national bank Friday and also approved a modest deployment of U.S. troops to the Middle East to bolster Saudi Arabia's defensive capabilities. Secretary of Defense Mark Esper emphasized the move was "defensive in nature."

Iran’s foreign minister, Javad Zarif, dismissed the U.S. troop deployment as “posturing” and expressed no optimism for a de-escalation in U.S-Iran tensions, even as world leaders gathered in New York for high-level meetings at the United Nations.

“I think it's all going the wrong direction in addressing this issue, Zarif told CBS in an interview that aired Sunday. "I don't think this type of posturing helps."

Zarif said Iran played no role in the attacks on Saudi Arabia. The Houthis, an Iranian-backed rebel group at war with Saudi Arabia, have claimed responsibility for the strikes.

But Pompeo and others have said the Houthis do not possess the kind of sophisticated weaponry used in the attacks, and they say evidence shows the strikes came from the north, not from Yemen.

Still, Pompeo would not say if the U.S. could prove definitely that the attacks were launched from Iranian territory. Pressed on that question, he said the weapons used in the attack were Iranian-made but avoided a direct answer about the launch site.

"The United States will respond in way that reflects that act of war by this Iranian revolutionary regime,” he said, suggesting the Trump administration is considering additional steps.

Even as Pompeo spoke of retaliation, Trump declined to rule out a meeting with Iranian President Hassan Rouhani on the sidelines of the UN meetings. Speaking to reporters Sunday morning as he left the White House for Texas, Trump said he had no plans to meet Rouhani but added that “nothing is ever off the table.”

Zarif said earlier this week that Iran does not want a military conflict with the U.S., but the country will defend itself if attacked. Any strike by the U.S. or Saudi Arabia, he warned, would result in an "all-out war."

Zarif and Pompeo were both in New York, along with dozens of other presidents and prime ministers from across the globe, as the United Nations prepares for its 74th annual general assembly.

Trump administration officials hinted that they might bar Zarif and Rouhani from attending the UN session, but the two Iranian leaders were granted visa waivers just days before the UN meetings were set to begin.

“They want me to know that I'm not supposed to be here,” Zarif told CBS.

The Trump administration slapped sanctions on Zarif in July, after he rejected an invitation to meet with President Donald Trump at the White House.

Iranian leaders have suggested Trump only wants a photo-op and is not serious about negotiating a substantive negotiation that could reverse an increasingly hostile relationship between the two countries.

Tensions between the U.S. and Iran have been spiraling since last year, when Trump withdrew the U.S. from a multi-lateral agreement to curb Iran's nuclear program. The Trump administration has slapped an escalating series of sanctions on Iran since then, aiming to choke Iran's economy and force its leaders into a new round of negotiations.

Contributing: David Jackson and Michael Collins