Terry Lloyd's daughter, Chelsey, and his wife, Lynn , made statements after the inquest.
Chelsey Lloyd said: "We have waited for three and a half years to hear the truth of how and why my father died whilst trying to report the war for millions of viewers back home.
"Finally in the last few days, with the help of ITN and British military police investigations, we have heard and seen evidence which proves without doubt that my father was unlawfully killed by a bullet to the head from a heavy calibre machine-gun fired by US Marines.
"The killing of my father would seem to amount to murder which is deeply shocking.
"We call on the Attorney General and the DPP to commence proceedings to bring the soldiers, including their commanding officers, to justice.
"They did not come to this inquest to explain their actions let them now do so in our criminal courts where they are guaranteed to get a fair trial.
"The value of inquests has been demonstrated in this case. Until now, we were unaware that my father was able to stand and walk to a makeshift ambulance after being shot once by an Iraqi bullet.
"The man who stopped to help my father was an ordinary Iraqi, whose intentions were to take him and other wounded to a nearby hospital.
"After helping my father into his minibus the evidence shows that the vehicle, whilst driving the wounded away, was fired on by US forces and that one bullet entered my father's head, after passing through the vehicle, and it was this American bullet which killed him.
"Many questions remain unanswered including why the US forces fired on the two ITN vehicles with deadly firepower, what happened to Fred Nerac and Hussein Osman, my father's colleagues. What were the standing orders and the rules of engagement of the US Marines and why is there 15 minutes of film missing which we believe would show the moments when the two ITN vehicles came under fire and my father making his way to the minibus and it coming under fire?
"I want to thank the many people who helped me and my family get to the stage we have reached today: ITN for its unstinting support throughout, in particular Nick Walshe, Glenda Gaitz, Angela Frier, David Mannion, editor in chief, and Stewart Purvis, formerly ITN's chief executive. The investigating team was crucial in helping establish the truth.
"Daniel Demoustier, who came and told us exactly what happened both in the build up and in the attack itself.
"Major Kay Roberts for uncovering so many witnesses and vital evidence and Soldier B who was an eye witness to the attack on the two ITN vehicles.
"All the forensic scientists and pathologists who gave evidence to the court in particular Mr Warlow whose evidence concerning the bullet fragments was crucial.
"I also want to thank the man who tried to save my father's life by taking him to hospital in Basra. He was just the kind of man my father was trying to help in reporting the war neutrally with an emphasis on how it was affecting ordinary Iraqis."
Here is the statement read by solicitor Louis Charalambous on behalf of Lynn Lloyd.
"Lynn Lloyd, Terry's widow, who asks for her privacy to be respected at this time, has asked me to pay tribute to the rest of her husband's team; Daniel Demoustier, Hussein Osman and Fred Nerac, who remains missing, and to the Iraqi man who put his own life at risk to try to save her husband's life. She also thanks the National Union of Journalists for their support over the last three and a half years.
"Painful as it has been, she is relieved that the truth has finally emerged thanks to the efforts of so many and echoes the Coroner's report that he will write to the DPP and the Attorney General to bring the prepetrators to justice.
"Terry Lloyd was, in the words of Trevor McDonald, a journalists' journalist.
"He had reported on wars for 20 years when he was killed lying in the back of a makeshift ambulance.
"The evidence heard in this court establishes that the cirumstances of his death from an American bullet whilst being ferried to hospital is a very serious war crime. How else can firing on a vehicle in these circumstances be interpreted?
"The evidence of how Terry Lloyd was unlawfully killed has shown that this was no, I wish to stress, friendly fire, blue-on-blue, incident or a crossfire incident.
"It was a despicable, deliberate and vengeful act particularly as it came after the end of the initial exchanges in which Mr Lloyd was hit by an Iraqi bullet.
"The verdict of unlawful killing was inescapbale and came about because US forces appear to have allowed their soldiers to behave like trigger-happy cowboys in an area in which there were civilians travelling on a highway, both Iraqi and European.
"The Marines who fired on civilians and those gave those orders should now stand trial. Under the Geneva Conventions Act, that trial should be for the murder of Terry Lloyd and nothing else."