Tehran, Iran (CNN) The military adviser to Iran's Supreme Leader said Sunday that Tehran's response to the killing by the United States of its most most influential general will "for sure be military."

In an exclusive interview with CNN in Tehran, the adviser -- Maj. Gen. Hossein Dehghan -- made the most specific and direct threat yet by a senior Iranian official following the killing of Gen. Qasem Soleimani in a US drone strike in Baghdad.

Dehghan said Iran would retaliate directly against US "military sites."

Dehghan is a former defense minister and is now the main military adviser to Ayatollah Ali Khamenei. He told CNN that reprisals would come from Iran itself, not its allied militia in the region.

"It might be argued that there could be proxy operations. We can say America, Mr. Trump, has taken action directly against us -- so we take direct action against America."

The United States has a growing military presence in the region. Thousands of US troops have been deployed to Saudi Arabia, and there are some 5,000 at bases in Iraq. The US also has a major air base in Qatar and a naval presence in Bahrain, as well as troops stationed in Jordan, Kuwait and the United Arab Emirates.

In common with other Iranian officials, Dehghan suggested that Iran was in no hurry to retaliate and would choose its targets carefully. "Our reaction will be wise, well considered and in time, with decisive deterrent effect."

Iran's President Hassan Rouhani had earlier said that Americans would face consequences for killing Soleimani "not only today, but also in the coming years."

Given the rhetoric of both sides, there is a growing risk of escalation in what has become the most dangerous confrontation between the US and Iran in decades.

Late Saturday, President Donald Trump tweeted that "If Iran attacks an American Base, or any American, we will be sending some of that brand new beautiful equipment their way...and without hesitation!"

The President continued: "They attacked us, & we hit back. If they attack again, which I would strongly advise them not to do, we will hit them harder than they have ever been hit before!"

Dehghan responded defiantly to Trump's warning.

"It was America that has started the war. Therefore, they should accept appropriate reactions to their actions," he said.

"The only thing that can end this period of war is for the Americans to receive a blow that is equal to the blow they have inflicted. Afterward they should not seek a new cycle."

In recent months, officials in the Trump administration and even the President himself have floated the possibility of renewed dialogue with Iran. Dehghan dismissed that possibility.

"Look, for several reasons we didn't want to negotiate with this incumbent US administration. Now, after what happened to Mr. Soleimani there is no point for negotiations or relations. It's impossible."

Photos: US airstrike in Baghdad kills Iran's top general Mourners throng the car carrying the body of Iranian commander Qasem Soleimani during a funeral procession for Soleimani and Iraqi paramilitary leader Abu Mahdi al-Muhandis in Baghdad on January 4. Hide Caption 1 of 22 Photos: US airstrike in Baghdad kills Iran's top general Mourners touch a casket draped in Iranian flags during Qasem Soleimani's funeral procession on January 4. Hide Caption 2 of 22 Photos: US airstrike in Baghdad kills Iran's top general This photo, released by the Iraqi Prime Minister Press Office, shows a burning vehicle at the Baghdad International Airport following the US airstrike that killed Gen. Qasem Soleimani, the head of Iran's elite Quds Force, on January 3. Hide Caption 3 of 22 Photos: US airstrike in Baghdad kills Iran's top general People watch debris burn near the airport after the airstrike on January 3. Hide Caption 4 of 22 Photos: US airstrike in Baghdad kills Iran's top general Pro-Iranian militiamen and their supporters set a fire while US soldiers shoot tear gas during a demonstration outside the US Embassy in Baghdad, Iraq, on Wednesday, January 1. Hide Caption 5 of 22 Photos: US airstrike in Baghdad kills Iran's top general A protester inspects the burnt-out entrance of the US Embassy on January 1. Hide Caption 6 of 22 Photos: US airstrike in Baghdad kills Iran's top general US Marines stand guard on the roof of the US Embassy while protesters demonstrate on Wednesday. Hide Caption 7 of 22 Photos: US airstrike in Baghdad kills Iran's top general Protesters set fire to a reception room of the US Embassy in Baghdad, Iraq, on Tuesday, December 31. The embassy was attacked during demonstrations in response to recent airstrikes in Iraq and Syria conducted by US forces. Hide Caption 8 of 22 Photos: US airstrike in Baghdad kills Iran's top general US Marines from a crisis response task force based in Kuwait prepare to deploy to Baghdad to bolster security at the embassy. Hide Caption 9 of 22 Photos: US airstrike in Baghdad kills Iran's top general A US Army Apache helicopter drops flares over Baghdad in a show of force. Hide Caption 10 of 22 Photos: US airstrike in Baghdad kills Iran's top general Protesters carry the logo of the US Embassy. Hide Caption 11 of 22 Photos: US airstrike in Baghdad kills Iran's top general Smoke billows from a sentry box at an entrance of the embassy. Hide Caption 12 of 22 Photos: US airstrike in Baghdad kills Iran's top general Protesters throw stones toward the embassy. Hide Caption 13 of 22 Photos: US airstrike in Baghdad kills Iran's top general US soldiers take positions around the embassy during the protests. Hide Caption 14 of 22 Photos: US airstrike in Baghdad kills Iran's top general Protesters burn property in front of the embassy compound. Hide Caption 15 of 22 Photos: US airstrike in Baghdad kills Iran's top general People are seen through thick tear gas after protesters breached the outer wall of the embassy. Hide Caption 16 of 22 Photos: US airstrike in Baghdad kills Iran's top general A picture taken through a broken window shows a vandalized room in the embassy. Hide Caption 17 of 22 Photos: US airstrike in Baghdad kills Iran's top general US soldiers stand guard inside the embassy. Hide Caption 18 of 22 Photos: US airstrike in Baghdad kills Iran's top general Protesters and militia fighters smash the bullet-proof glass of the embassy's windows with blocks of cement after breaching the outer wall. Hide Caption 19 of 22 Photos: US airstrike in Baghdad kills Iran's top general Iraqi security forces stand guard as protesters, including clerics, hold a prayer inside the walls of the embassy. Hide Caption 20 of 22 Photos: US airstrike in Baghdad kills Iran's top general Iraqi security forces stand guard at the entrance of embassy. Hide Caption 21 of 22 Photos: US airstrike in Baghdad kills Iran's top general Mourners carry the coffins of Iranian-backed paramilitary fighters in Najaf, Iraq, on December 31. The fighters were killed in US airstrikes on Sunday that sparked Tuesday's attacks on the US Embassy in Baghdad. Hide Caption 22 of 22

'Gangster and a gambler'

Dehgahn also responded to Trump's threat to include Iranian cultural sites among 52 targets the US had selected to strike in the event of Iranian retaliation. The number was chosen to match the number of hostages taken in the 1979 takeover of the US Embassy, Trump said.

Dehghan said the tweets were ridiculous and absurd. "If he says 52 we say 300 -- and they are accessible to us," Dehghan said. "No American military staff, no American political center, no American military base, no American vessel will be safe.

"He doesn't know international law. He doesn't recognize UN resolutions either. Basically he is a veritable gangster and a gambler."

At one point in the interview, Dehghan pulled out a picture of Soleimani and held it up to the camera.

"All Iranians are Qasem Soleimani," he said, and insisted the Quds force, which Soleimani had led since 2003, would not be weakened by his death. The Quds have been responsible for projecting Iranian influence across the Middle East and beyond and have played a major role in supporting the Assad regime in Syria.

"The person who has replaced him has been cooperating with him for two decades. He has the same manner and method," Dehghan said.

Iran's will to defend its interests "has increased a thousand times. We don't feel anything. We have a logic, the logic of martyrdom."

As the war of words escalates, Dehghan echoed the comments of other senior Iranian officials that the country was not seeking war.

"Let me tell you one thing: Our leadership has officially announced that we have never been seeking war and we will not be seeking war."

But his demand that the US not respond to any reprisals by Iran for Soleimani's killing will surely fall on deaf ears. This cycle of violence accelerated when a US contractor was killed in a rocket attack on a joint US-Iraqi military base on December 29th.

US officials held a pro-Iranian militia responsible for the attack. Its leader was killed along with Soleimani in the US drone strike in Baghdad.