Mr Corbyn has written to the Prime Minister to ask seven questions, including what the UK Government knew ahead of the air strike which killed General Qassem Soleimani, if there was an increased terror risk in the UK and whether Boris Johnson had spoken to US president Donald Trump.
It is understood there are no plans to send more British troops to the region and Foreign Secretary Dominic Raab has called for a calming of tensions from all sides.
General Soleimani, the head of Tehran’s elite Quds Force who spearheaded military operations in the Middle East, was targeted in an attack at Baghdad’s international airport on Friday.
Mr Raab discussed the dramatic ratcheting of tensions with Mr Trump’s Secretary of State Mike Pompeo later in the day.
In his letter to Mr Johnson, outgoing Labour leader Mr Corbyn also asked if the UK had spoken to the UN “to discuss consequences for peace and security” and what measures had been taken to “ensure the safety of UK nationals”.
He said: “Given the serious nature of the issues now faced by our country and indeed the world as a consequence of the US attack, I would welcome a prompt response to this request and stand ready to attend any briefing meeting as soon as arranged.”
The Prime Minister is currently on holiday on the private Caribbean island of Mustique with his girlfriend Carrie Symonds and Number 10 has yet to confirm when the pair are due to return to Downing Street.
But there was criticism of the US for apparently not giving warning of the attack to the UK, which has hundreds of troops deployed in Iraq.
Mr Corbyn described the strike as an “assassination” and called on the Government to stand up to the “belligerent actions” from the US.
The US president said Gen Soleimani was targeted because he was “plotting to kill” many Americans and that he “should have been taken out many years ago”.
Mr Trump said a “reign of terror is over” and accused the general of making “the death of innocent people his sick passion”.
Iran’s Supreme Leader Ayatollah Ali Khamenei warned that “severe revenge awaits the criminals” behind the strike and announced three days of national mourning.
Mr Raab issued a statement saying the Government had “always recognised the aggressive threat posed by the Iranian Quds force” led by the general.
“Following his death, we urge all parties to de-escalate. Further conflict is in none of our interests,” Mr Raab added.
The Secretary of State thanked Mr Raab in a phone call for recognising the “aggressive threats posed” by the Quds Force in his statement, according to US spokeswoman Morgan Ortagus.
Mr Pompeo was also said to have stressed that the White House “remains committed to de-escalation”.
Prominent Tory MP Tom Tugendhat, who was chairman of the Foreign Affairs Committee in the last Parliament, was critical of the US for not giving the UK warning of the attack, though the Government did not confirm it was not briefed in advance.
He urged the White House to “share much more closely with allies” in the future, adding to the BBC that “the purpose of having allies is that we can surprise our enemies and not each other”.
The Ministry of Defence (MoD) said there were around 400 British troops deployed in Iraq as part of the UK’s fight against the Islamic State terror group.
A further 500 personnel are based at RAF Akrotiri in Cyprus which flies fast jets and reconnaissance planes over Iraq and Syria, the MoD added.
Earlier, Mr Corbyn said: “The UK Government should urge restraint on the part of both Iran and the US, and stand up to the belligerent actions and rhetoric coming from the United States.
“All countries in the region and beyond should seek to ratchet down the tensions to avoid deepening conflict, which can only bring further misery to the region, 17 years on from the disastrous invasion of Iraq.”
Emily Thornberry, the shadow foreign secretary bidding to become the next Labour leader, criticised the Prime Minister for having “pathetically unopposed” Mr Trump’s decision to pull out of the Iran nuclear deal.
Other potential Labour leaders also weighed in on the attack, with shadow Brexit secretary Sir Keir Starmer calling it an “extremely serious situation” and urging the UK to “engage, not isolate Iran”.
Tory MP Tobias Ellwood, a former defence minister who served as a captain in the Army, tweeted “this is big”, adding: “Expect repercussions.”
The Foreign Office advises British-Iranian dual nationals against all travel to Iran and for other British nationals to seek the department’s advice before travelling to the nation.
British nationals risk being arbitrarily detained or arrested by Tehran, the department warned.
Nazanin Zaghari-Ratcliffe has been among the dual nationals being held in Iran since she was arrested in 2016 and accused of spying while visiting family.
Her husband Richard Ratcliffe told ITV’s Good Morning Britain: “I sit here partly worried for what that means for Nazanin, partly worried what that means for my in-laws, sat in their ordinary living room in Tehran where they’re all really worried.”