The United States has agreed to release a classified cockpit video showing the reaction of two American pilots after they killed a British soldier during a friendly fire incident in Iraq, a spokesman for the coroner said Tuesday.

In the video, a U.S. pilot is heard saying "I'm going to be sick," then "we're in jail, dude," after firing on the convoy in the southern Iraqi city of Basra on March 28, 2003. Lance Cpl. Matty Hull was killed.

The U.S. military had previously refused to release the video to Hull's family, despite requests by British government officials and the coroner investigating the death. The video was leaked and published Tuesday by The Sun newspaper.

As a result, the U.S. had decided the video "can be shown to the coroner and the family in the presence of someone from the (Ministry of Defense)," coroner's officer Geoff Webb said.

At the Pentagon, spokesman Bryan Whitman said the U.S. military's own investigation concluded that the firing was accidental; that the pilots "followed the procedures and processes for engaging targets," and that as a result no disciplinary action was taken against them.

He said he was not certain whether U.S. Central Command, which led the investigation, had publicly released those findings.

The coroner said the leak means that the material is now in the public domain, suggesting it may be shown when in the inquest resumes Feb. 16.

VIDEO: Click Here to View Footage Obtained Exclusively by The Sun

"The main thing to stress is that we have always had a very clear view that what matters is the information should be available to the family and — whilst the Americans cannot be legally obliged to help — they should do so, bearing in mind they are our allies," said Constitutional Affairs Secretary Harriet Harman, who has had several meetings with officials in the U.S. Embassy.

The deputy chief of mission at the U.S. Embassy in London, David Johnson, told the British Broadcasting Corp. it would consider de-classifying the video if the military determined it would not put forces at risk.

The Ministry of Defense said in a statement Tuesday it had not tried to deceive Hull's family. It said the army's Board of Inquiry used a copy of the video in its investigation of the incident, but it was U.S. government property and it was not authorized to release it.

The pilot can be heard in the cockpit trying to establish whether targets on the ground are coalition forces or insurgents.

One man asserts that orange panels on the vehicles could mean they are coalition forces — most are equipped with bright markers to prevent such incidents.

Another man is heard saying the orange markers look like rockets.

"I think killing these damn rocket launchers, it would be great," a man on the recording is heard saying.

Two U.S. A-10 jets allegedly opened fire on Hull's tank, which was part of five-vehicle convoy engaged in combat outside of Basra. Four other soldiers were injured, including the convoy's leader, Capt. Alexander MacEwen.

The convoy — three British Scorpion tanks and two engineering vehicles — had come to a halt at the edge of a shantytown near the southern Iraqi city of Basra. The soldiers were being approached by a crowd of civilians carrying a white flag when they were attacked.

The transcript printed in The Sun records the alleged exchange between the pilots after they realize what has happened.

Pilot 1: "I'm going to be sick."

Pilot 2: "Ah f—-."

Pilot 1: "Did you hear?"

Pilot 2: "Yeah, this sucks."

Pilot 1: "We're in jail, dude."

The other pilot then weeps, according to the transcript.

"There has never been any intention to deliberately deceive or mislead Lance Corporal Horse Hull's family," the defense statement said.

The ministry said when army told the family the findings of its investigation, "we did inform them that some classified material had been withheld, but we did not specify its exact nature."

The coroner investigating Hull's death has adjourned the inquest until Feb. 16.

A U.S. Air Force official conducted its own investigation into the incident in 2003, but the results of that investigation were not publicly released, said Lt. Tony Vincelli, spokesman for the Boise, Idaho-based 190th Fighter Squadron, where the A-10 jets are based.

The investigation did not result in a court-martial. Vincelli did not identify the pilots involved.

It is unclear whether the video will be shown at the inquest.

"It is in the public domain, there's no dispute of that is there? It's all over the television," said Geoff Webb, a coroner's court official.

The Sun is owned by News Corp., which is the parent company of FOXNews.com.