Senior members of the Trump administration upped the ante against Iran over the weekend, revealing a warning sent to Revolutionary Guard commander Qassem Soleimani and promising a regional strategy to roll back Tehran’s proxies across the Middle East.

CIA director Mike Pompeo and national security adviser HR McMaster spoke at length about Iranian expansion in “weak states” in the Middle East at the 2017 Reagan National Defence Forum in California on Saturday.

Mr Pompeo, who leads the list of contenders to possibly replace Rex Tillerson as secretary of state, confirmed that he sent a letter recently to Maj Gen Qassem Soleimani, head of the Iranian Revolutionary Guard's foreign operations arm.

"I sent a note. I sent it because he had indicated that forces under his control might in fact threaten US interests in Iraq," the CIA chief said.

"He refused to open the letter. It 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 for any attacks on American interests in Iraq by forces that are under their control. We wanted to make sure he and the leadership in Iran understood that in a way that was crystal clear."

Referring to the changing dynamic in Iraq after the Kurdish independence referendum and the Revolutionary Guard's most recent presence in Kirkuk, he said: “You need to only look to the past few weeks and the efforts of the Iranians to exert influence in northern Iraq, in addition to other places in Iraq, to see that Iranian efforts to be the hegemonic power throughout the Middle East continues to increase.”

Last week the semi-official Iranian news agency Fars quoted Mohammad Golpayegani, a senior Iranian official, as saying that a CIA representative sent a letter to Gen Soleimani when he was in the Syrian town of Albu Kamal last month, supervising the battle against ISIL.

“I will not take your letter nor read it and I have nothing to say to these people,” Mr Golpayegani quoted Maj Gen Soleimani as saying.

Mr McMaster also struck a hawkish tone on Iran at the forum, which was being held two months after Mr Trump announced his strategy of decertifying the Iran nuclear deal and countering Tehran regionally.

“What the Iranians have done across the Middle East is fuel and accelerate cycles of violence so that they can take advantage of chaos and weak states to make them dependent on Iran for support,” the national security adviser said.

He assigned blame to the Obama administration without mentioning it by name. “In recent years, what we can say in retrospect, it was unrealistically hopeful [US] strategy that, given the nuclear deal - that this president called worst deal ever - that this deal will result in an Iran that would integrate effectively in region. The exact opposite happened,” Mr McMaster said.

“The fact that we were trying to accommodate Iran has empowered Iran across the globe, and when president says he inherited a mess that is in greater Middle East, we have to address growing Iranian capability, and their use of militias, proxies and terrorist organisation.”

Mr McMaster accused Iran of seeking “hegemonic aims" in the region.

He said Tehran was "using a campaign of subversion in Iraq" and providing support for president Bashar Al Assad of Syria, where "about 80 per cent of Assad fighters are Iranian proxies in Syria to establish a land bridge over into the Mediterranean”.

The threat in particular is the “prospect of Iran having a proxy army on the borders of Israel. What we see is weaponisation of Iran's network in Yemen and in southern Lebanon,” he said.

Arabic media outlets reported over the weekend that Israel struck an “Iranian base” in Syria on Saturday. Neither Iran nor Israel confirmed such attack.

"What we have in place now is a comprehensive strategy for Iran, and denying Iran all access to a nuclear weapons is one part of that strategy," Mr McMaster said. "Countering behaviour is another critical part of the strategy."

Jonathan Schanzer, vice president of research at the Foundation for Defense of Democracies, told The National that “the intent [to counter Iran] is there” but “the implementation is now the key”.

“Can this administration rally the relevant government agencies to engineer a broad pushback on Iran’s regional aggression? We’ll find out in the months ahead, particularly as ISIL melts away and Tehran seeks to fill the void in Iraq and Syria.”