The US has blamed Iranian-affiliated militias for Wednesday's rocket attack in Iraq that killed two Americans and a British soldier.
Kataib Hezbollah is the only group known to have the capabilities for an attack of this scale, Gen Kenneth McKenzie, head of US Central Command, said on Thursday in a meeting of the Senate armed services committee.
Hours after the attack, air strikes in eastern Syria killed 26 Iraqis from an Iran-backed militia.
Iraq's military command described the attacks as "a serious security challenge" and have pledged to investigate.
The Syrian Observatory for Human Rights said three warplanes bombed Hashed Al Shaabi bases near the border town of Albu Kamal. It is not yet known who conducted the strikes.
Western intelligence sources say the border town is on a supply route for Iran-backed militias who regularly send reinforcements from Iraq into Syria to aid President Bashar Al Assad's forces.
"Ten explosions shook the area," the monitor's head, Rami Abdulrahman, said from Britain.
Eighteen rockets hit the Taji airbase north of Baghdad on Wednesday. It hosts troops from the US-led coalition helping local forces to battle extremists.
The coalition said three of its personnel were killed and 12 wounded.
“It is with deep sadness that I learnt that a UK soldier was killed in the attack at the Taji military base last night," UK Prime Minister Boris Johnson said on Thursday.
"My thoughts go out to their loved ones at this extremely difficult time.
“We will continue to stay in close contact with our coalition partners to establish exactly what happened."
The soldier has been identified as Lance Corp Brodie Gillon, 26, of the reserve with the Scottish and North Irish Yeomanry.
Corp Gillon's commanding officer described her as a "larger-than-life soldier who was determined to deploy on operations, help others, develop herself and gain practical experience".
US Secretary of State Mike Pompeo and British Foreign Minister Dominic Raab also condemned the attack.
They stressed "that those responsible for the attacks must be held accountable", the US State Department said.
Mr Raab said the Iraqi authorities must find who was responsible for the attack.
“My heartfelt condolences to the families of those killed in this cowardly attack," he said.
“We must find those responsible. I welcome the Iraqi President’s call for an immediate investigation to hold perpetrators to account but we must see action.”
Iraqi security forces later found the launch vehicle, converted to fire Katyusha rockets believed to have been used in the attacks.
Iraqi President Barham Salih and Parliamentary Speaker Mohammed Al Halbusi condemned the "terrorist attack" on "Iraq and its security".
The UN mission in Iraq called for "maximum restraint on all sides".
"These ongoing attacks are a clear and substantial threat to the country, and the risk of rogue action by armed groups remains a constant concern," it said.
"The last thing Iraq needs is to serve as an arena for vendettas and external battles."
Officials said it was too early to assign blame for the latest strike, but any indication that Iran-backed militia were responsible could ignite more escalation between the US and Iran.
Two days after the death of an American after rockets were fired on an Iraqi military base in Kirkuk at the end of last year, the US army hit five bases in Iraq and Syria used by the pro-Iran militia Kataib Hezbollah.
Tensions rose further between Washington and Tehran, leading to the assassination in Baghdad on January 3 of powerful Iranian commander Qassem Suleimani and Abu Mahdi Al Muhandis, head of Kataib Hezbollah.
Iran retaliated by launching missiles at an Iraqi base hosting US soldiers days later.
The US leads an international coalition made up of dozens of countries and thousands of soldiers, which was formed in Iraq in 2014 to fight ISIS.
While the extremist group has lost its territory, sleeper cells are capable of carrying out attacks.
The Iraqi Parliament voted to expel all foreign soldiers from the country after Suleimani was killed, a decision that must be approved by the government.
The departing government, which resigned in December amid mass protests, has yet to be replaced because of a lack of agreement in Parliament.