Beirut, Lebanon (CNN) As the dust settles, part of Iran's response to the killing of its top general by the United States seems to be pushing President Donald Trump to do what he's always wanted to in the Middle East: leave.

One message is coming from Iran and its allies (from Qasem Soleimani's daughter to Iran's foreign minister and the head of Hezbollah in Lebanon): the end of the US presence in the region has started.

"Our aim is clear. The response to [shedding] the blood of Qasem Soleimani and Abu Mahdi [al-Muhandis] is driving out US forces from our entire region," Hassan Nasrallah, the leader of the Iranian-backed Lebanese militant group, said in a speech at a memorial rally in Beirut on Sunday.

That's a tall, if not impossible, order. And Iran's military planners must surely have entered at least a brief period of recalibration around who they could trust and telephone safely after seeing their top military commander unexpectedly killed by a US drone strike outside the main airport of a friendly capital city.

Yet Iran compensates for its lack of military might -- compared to the US -- with shrewd tactics and affiliated militant groups to retaliate for them. And here they are hitting on an objective that Trump has himself espoused, albeit voluntarily.

Iraq has kicked off the process, its parliament asking the executive Sunday to force the departure of the US military and all coalition forces. These calls may dissipate over time, perhaps, but America's Commander in Chief is hardly cooling tempers by threatening unprecedented sanctions on Iraq in response and even demanding billions of dollars of repayment for airbases built there before it exits.

A new mission

However considered the decision to kill Soleimani was, Trump's off-the-cuff rhetoric, on and off his Twitter feed, is doing Iran's job for them by fomenting anger at the US.

Slowly across the region, more militants will likely emerge claiming their mission is to send US troops home in coffins, in very much the same way Hezbollah's Nasrallah threatened on Sunday.

Nasrallah even hinted at a sustained campaign that would focus on Trump's chances of re-election later this year.

This is where an Iranian strategy might find some success. They are to some extent pushing an open door. In the past, Trump has called Syria "sand and death" and repeatedly said that it's time to bring home US troops in the region.

Iranian violence may force Trump to resist these instincts initially -- as with Sunday's rhetoric about Iraq -- but in the longer term this is what his White House has wanted to do.

Photos: Iranians mourn Qasem Soleimani Mourners carry the coffin of Gen. Qasem Soleimani during a funeral procession in his hometown of Kerman, Iran, on Tuesday, January 7. Hide Caption 1 of 19 Photos: Iranians mourn Qasem Soleimani Relatives of victims that were caught in a stampede wait outside a hospital in Kerman on January 7. Hide Caption 2 of 19 Photos: Iranians mourn Qasem Soleimani A portrait of Soleimani hangs outside a hospital where victims of the stampede were being treated. Hide Caption 3 of 19 Photos: Iranians mourn Qasem Soleimani Relatives check a list of stampede victims at a hospital in Kerman. Hide Caption 4 of 19 Photos: Iranians mourn Qasem Soleimani A vehicle carrying Soleimani's remains makes its way through a crowd in Kerman. Hide Caption 5 of 19 Photos: Iranians mourn Qasem Soleimani Mourners view the funeral procession from a bridge in Kerman. Hide Caption 6 of 19 Photos: Iranians mourn Qasem Soleimani The coffins of Soleimani and others killed in the US airstrike are carried on a truck during the final leg of the funeral procession on January 7. Hide Caption 7 of 19 Photos: Iranians mourn Qasem Soleimani Mourners in Kerman wear scarves depicting Soleimani. Hide Caption 8 of 19 Photos: Iranians mourn Qasem Soleimani Soleimani's funeral continued in the northeastern city of Qom on Monday, January 6. Hide Caption 9 of 19 Photos: Iranians mourn Qasem Soleimani Thousands of mourners took part in a funeral procession in Tehran on January 6. Hide Caption 10 of 19 Photos: Iranians mourn Qasem Soleimani Gen. Ismail Qaani — Soleimani's longtime lieutenant and his successor as the leader of the Quds Force — cries over Soleimani's coffin during the funeral on January 6. Hide Caption 11 of 19 Photos: Iranians mourn Qasem Soleimani Mourners hold Soleimani posters during his funeral in Tehran. Hide Caption 12 of 19 Photos: Iranians mourn Qasem Soleimani Iranian President Hassan Rouhani, fourth from left, and Supreme Leader Ayatollah Ali Khamenei, fifth from left, attend the funeral in Tehran. Hide Caption 13 of 19 Photos: Iranians mourn Qasem Soleimani Solemani's daughter Zainab makes a speech during her father's funeral. Hide Caption 14 of 19 Photos: Iranians mourn Qasem Soleimani Crowds fill the streets of Tehran during Soleimani's funeral procession. Hide Caption 15 of 19 Photos: Iranians mourn Qasem Soleimani People carry placards and flags during the funeral procession. Hide Caption 16 of 19 Photos: Iranians mourn Qasem Soleimani Revolutionary Guard members accompany the coffins. Hide Caption 17 of 19 Photos: Iranians mourn Qasem Soleimani Former Iranian President Mahmoud Ahmadinejad, third from right, attends Soleimani's funeral. Hide Caption 18 of 19 Photos: Iranians mourn Qasem Soleimani Iranians set a US and an Israeli flag on fire during the funeral procession. Hide Caption 19 of 19

A US departure from Iraq alone would be a huge strategic win for Iran, possibly commensurate retaliation to the loss of Soleimani. The US's presence in Syria would be immediately endangered, without a land border with Iraq to resupply troops from.

It means the US would lose the presence it has to the west of Iran while it's slowly trying to leave to the east -- Trump simultaneously wants to leave Afghanistan, preferably after a peace deal with the Taliban (who have in the past received Iranian help, according to the US).

This may not be all Iran does.

A flare-up between its proxies and traditional US allies in the region (like Hezbollah and Israel and the Houthis and Saudi Arabia) remains possible. But rhetoric to this effect has been muted, so far.

It is also feasible that Iran could hit softer US targets globally, like diplomats outside of the region, or civilians. But Nasrallah went out of his way to make it very clear he does not want to see US citizens attacked.

"They cannot be touched... any harm to US civilians will only serve Trump's agenda," he said.

A cyberattack is something also western intelligence agencies have warned about.

JCPOA

But Iran has only actually done one thing in response to the killing so far, and it may be of the greatest long-term significance. It has said it will no longer abide by its key remaining commitment on enrichment under the nuclear deal.

It is unclear precisely what level of enrichment Iran may now seek, yet that is entirely the point.

When Iran signed the nuclear deal, it would be naive to think part of its elite did not have a plan for what it would do if the deal fell apart and they wanted to race for a nuclear bomb.

Estimates before the deal was signed in 2015 said it would take Iran about a year, or less, to "breakout" for a viable device if it chose to, according to multiple analysts.

If they choose to engage in this, or are already doing so, it will be done with great secrecy. Broadcasting any move would invite Israeli and US airstrikes on nuclear sites.

If Tehran is seeking to memorialize the death of Soleimani by changing the balance of power in the region, Iran's first nuclear test would overwhelmingly achieve that.

A slow drip of US military casualties would also impact on those parts of the US electorate that saw the Soleimani strike as a wise deployment of American might by Trump's White House.

Iran has yet to loudly, publicly and violently respond to the attack with a speed that fits into Trump's 24-hour cable news diet. But that may be cause for greater concern, not relief.