Top Iranian officials on Sunday denied involvement in the recent attacks on Saudi Arabian oil infrastructure and issued new threats to the U.S. and its allies, vowing “the full destruction of any aggressor” that tests Tehran.

The warnings came on the heels of Friday’s announced deployment of more U.S. troops to the Middle East. The move, military officials said, is designed as a deterrent against an increasingly hostile Iran.

Trump administration officials on Sunday issued their own warnings to Iran, stressing that the U.S. will not hesitate to defend itself while also saying they want to avoid military conflict and will continue pursuing a diplomatic track this week at the United Nations General Assembly in New York.

But Iran seems to have little appetite for diplomacy and instead is ramping up its rhetoric.

Maj. Gen. Hossein Salami, the head of Iran’s Islamic Revolutionary Guard Corps, said over the weekend that any “limited” military response by either Saudi Arabia or the U.S. will lead to widespread destruction.

“Be careful. A limited aggression will not remain limited. We will pursue any aggressor,” Gen. Salami said in a speech broadcast on Iranian state-controlled TV. “We are after punishment, and we will continue until the full destruction of any aggressor.”

The White House, the State Department and the Pentagon have gone to great lengths over the past week to avoid further inflaming tensions with Iran. So far, the administration has steered clear of retaliatory strikes against Iran after an attack earlier this month in Saudi Arabia’s Abqaiq oil facility, a key cog in global energy markets.

Amid lingering questions about how Saudi Arabia — which has purchased state-of-the-art defense equipment from the U.S. in recent years — was unable to detect and thwart the attack, American military officials said they will dispatch another contingent of troops to the region.

The exact number of military personnel headed to the Middle East is expected to be announced this week. At a hastily arranged press conference at the Pentagon on Friday evening, Defense Secretary Mark Esper said the deployment will serve three distinct purposes.

“First, to send a clear message that the United States supports our partners in the region. Second, to ensure the free flow of resources necessary to support the global economy,” Mr. Esper told reporters. “And third, to demonstrate our commitment to upholding the international rules-based order that we have long called on Iran to obey.

“As the president has made clear, the United States does not seek conflict with Iran. That said, we have many other military options available should they be necessary,” the Pentagon chief added.

Mr. Esper and other administration officials have blamed the Abqaiq assault on Iran, though they have not said definitively that the missiles and drones used in the attack were launched from inside Iran.

Secretary of State Mike Pompeo said Sunday that the presence of more U.S. troops will help security conditions in the region and dissuade Iran from launching further attacks.

“It’ll improve,” Mr. Pompeo told ABC’s “This Week.” “It’s about volume and density.”

But Iran continues to deny responsibility for the Abqaiq attack. Iranian Foreign Minister Javad Zarif told CBS’s “Face the Nation” on Sunday that he welcomes an investigation into the origins of the incident.

“I’m confident that Iran did not play a role. I’m confident that anyone who conducts an impartial investigation will reach that conclusion,” he said.

Mr. Zarif also said there will be no “limited war” in the region and that any conflict will end with the destruction of Iran’s enemies.

“I’m not confident we can avoid a war. I’m confident we will not start one,” he said. “But I’m confident whoever starts one will not be the one who finishes it.”

The administration dismissed Mr. Zarif’s comments.

“I don’t know why anyone listens to the Iranian foreign minister,” Mr. Pompeo said. “He has lied for decades. … It’s beneath the dignity of anyone in the world to listen to someone who repeatedly makes the claim that the Houthis launched this attack.”

Iran-backed Houthi rebels in Yemen have claimed responsibility for the Abqaiq attack. The U.S., Saudi Arabia and other nations have dismissed that claim.

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