The United States rebuffed an Iraqi request on Friday to prepare to pull out its troops, amid heightened US-Iranian tensions following the US killing of Iranian commander Qassem Soleimani.

Seeking to tighten pressure on its rival, the US, meanwhile, imposed more sanctions on Iran, responding to an attack on US troops in Iraq launched by Tehran in retaliation for the assassination of Soleimani.

Iraq looks set to bear the brunt of any further violence between neighbouring Iran and the US. Its leaders are caught in a bind as Washington and Tehran are also the Iraqi government's main allies and vie for influence there.

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Iraq's caretaker prime minister, Adel Abdul Mahdi, made his request in a phone call with US Secretary of State Mike Pompeo late on Thursday in line with a vote by Iraq's parliament last week, his office said in a statement.

Abdul Mahdi asked Pompeo to "send delegates to put in place the tools to carry out the Parliament's decision," it said, adding without elaborating, that the forces used in the killing had entered Iraq or used its airspace without permission.

However, the US State Department said any US delegation would not discuss the withdrawal of US troops as their presence in Iraq was "appropriate".

"There does, however, need to be a conversation between the US and Iraqi governments not just regarding security, but about our financial, economic, and diplomatic partnership," spokeswoman Morgan Ortagus said in a statement.

The latest flare-up in the long shadow-war between Iran and the US started with the killing of Soleimani in a US drone attack on January 3. Iran responded on Wednesday by firing missiles at US forces in Iraq.

In the aftermath, both sides backed off from intensifying the conflict but the region remains tense, with Iranian commanders threatening more attacks.

'Suffered enough from wars'

Iraq's top Shia leader on Friday condemned the US-Iranian confrontation taking place on Iraqi soil, saying it risked plunging an already war-ravaged country and the wider Middle East into deeper conflict.

Grand Ayatollah Ali al-Sistani said it was Iraqis who stood to suffer most from the US-Iranian conflict.

In a message delivered through a representative at Friday prayers in the holy city of Karbala, al-Sistani said no foreign powers should be allowed to decide Iraq's fate.

Iraqi Prime Minister Adel Abdul Mahdi speaking during a symbolic funeral ceremony of Major General Ali al-Lami, who commands the Iraqi Federal Police's Fourth Division [File: Khalid al-Mousily/Reuters]

"The latest dangerous aggressive acts, which are repeated violations of Iraqi sovereignty, are a part of the deteriorating situation" in the region, al-Sistani said.

Al-Sistani, who wields huge influence over public opinion in Iraq, only weighs in on politics during times of crisis and is seen as a voice of moderation.

"The people have suffered enough from wars ... Iraq must govern itself and there must be no role for outsiders in its decision-making," Sistani said.

Iraq has suffered decades of war, sanctions and sectarian conflict, including two US-led invasions and the rise and fall of al-Qaeda and ISIL (ISIS).

At Friday prayers in Tehran, an Iranian Muslim leader said US interests across the world were now exposed to threats.

"From now on, having too many bases, especially in this region, will not act as an advantage for them," Mohammad Javad Haj Aliakbari, a mid-ranking Muslim leader, told worshippers.

Since Soleimani's killing, Tehran has stepped up its calls for US forces to leave Iraq.

Iranian Supreme Leader Ali Khamenei has said the retaliatory attacks were not enough and that ending the US military presence in the region was Tehran's main goal.

Trump suggested on Thursday that Soleimani had been killed because he had planned to blow up a US embassy. He did not offer any evidence.

"Soleimani was actively planning new attacks and he was looking very seriously at our embassies and not just the embassy in Baghdad, but we stopped him and we stopped him quickly and we stopped him cold," Trump, who is seeking re-election this year, told a rally in Ohio.