The "heinous" attack on Erbil airport could destabilise the entire country, the UN's top official in Iraq said.
It came as the international community condemned Monday night’s rocket strikes that killed one person.
A civilian contractor died, and a US soldier was among at least nine people wounded.
The UN denounced the biggest attack on international forces in Iraq in months
Jeanine Hennis-Plasschaert, the top UN representative in Iraq, warned the country could spin out of control.
"Such heinous, reckless acts pose grave threats to stability," she said on Twitter, calling for "restraint" and co-operation between Baghdad and Erbil on a probe.
The attack was the first such assault on international forces in two months.
It heightens tensions after months of attacks on US forces following the killing of Iran's top general Qassem Suleimani and Iraqi militia leader Abu Mahdi Al Muhandis near Baghdad airport in January last year.
It was still unclear who carried out Monday night's attacks. A previously little known group claimed responsibility, yet to be verified, and Iran denied any involvement.
More than a dozen 107mm rockets were fired from around eight kilometres west of Erbil on Monday night.
US Secretary of State Antony Blinken said he was “outraged” by the attack and vowed to support the country’s efforts in holding those responsible to account.
"I have reached out to Kurdistan Regional Government Prime Minister Masrour Barzani to discuss the incident and to pledge our support for all efforts to investigate and hold accountable those responsible," he said.
UK Foreign Minister Dominic Raab said the attack on coalition forces and civilians in Erbil was “outrageous and unacceptable”.
A separate attack on a base near Baghdad last March killed a British soldier fighting with the international coalition against ISIS.
British Ambassador to Iraq Stephen Hickey said his country will support Baghdad and Erbil in finding the perpetrators after both sides announced a joint investigation into the attack.
“Strongly condemn the attack on the city of Erbil and Coalition forces last night,” Mr Hickey said on Twitter.
Coalition forces are in Iraq at the invitation of the Iraqi government, in order to fight ISIS, he said.
“These attacks terrorise civilians, destabilise Iraq, and undermine the fight against ISIS,” Mr Hickey said.
Canada’s ambassador to Iraq, Ulric Shannon, said he rejects the “cowardly” attack that harmed innocent civilians.
At least two of the wounded from Monday’s attacks were civilians near the airport at the time of the attack.
Mr Shannon expressed his country’s support towards Baghdad and Erbil investigations saying that there “needs to be stronger security co-ordination” between the two.
The UAE described the attack as “criminal” and said it rejected all forms of violence and terrorism that “aim to destabilise” the security and stability of states.
Reactions from inside of Iraq
The attack has caused significant concern in Erbil, Safeen Dizayi, head of Foreign Relations Department of Kurdistan Regional Government, told The National.
The Kurdistan region is not used to these “kinds of attacks and instability”, he said.
“Kurdistan has been renowned for its stability, coexistence, economic and political development, and prosperity. Therefore, when such incidents occur, it is of concern to the community, to the government, and to all those who live here, and also to our friends elsewhere in the international community in particular,” he said.
Mr Dizayi said it was vital for Baghdad and Erbil to co-operate to prevent such attacks from occurring again.
“We will be resilient, we will be adamant and we will overcome this for sure,” he said.
Relations between Erbil and Baghdad have been strained over the division of regional oil wealth, payments of salaries and demarcation of borders of the autonomous region.
KRG president Nechirvan Barzani called on the UN to work with Iraq to eliminate threats against civilians.
Masrour Barzani, prime minister of the KRG, also condemned the attack and urged Kurds to remain calm.
Iraqi President Barham Salih described the attack as a “terrorist act” that represented a “dangerous escalation”.
"We have no choice but to strengthen our efforts to root out the forces of terror and attempts to plunge the country into chaos," Mr Salih said on Twitter.
It is now a battle between "state and sovereignty against terrorism and outlaws," he said.
Iraqi Prime Minister Mustafa Al Kadhimi said the “terrorist act” aimed to create chaos across the country but the government is doing its best to combat such incidents.
“This terrorist act comes with great efforts made by the government to calm the situation in the region and to keep the country away from conflicts,” he said.
“Iraq will not be a sphere for it.”