Years ago, as the New Statesman's correspondent at a UN conference in Chile in the early 1970s, I chanced upon Robert McNamara, the former US defence secretary, in a narrow passage. "War criminal," I hissed as he went by. He looked hurt and confused; he must have suffered the same humiliation many times. Later, I came to regret my youthful gesture, as one of the principal architects of the US disaster in Vietnam sought to remake his life at the World Bank and to atone for the criminal decisions for which he will always be remembered. One reason for my change of heart was the release of White House tapes which showed the role McNamara had played in defusing the Cuban missile crisis of 1962. Another was the 2003 documentary film The Fog of War, in which McNamara drew intelligent lessons from the huge errors of Vietnam.

Yet, on reading Bernd Greiner's book, which casts a pitiless light on that most controversial of American wars, I wondered whether my original reaction had not in fact been correct. For among Greiner's conclusions is that McNamara and his colleagues were by no means wandering lost in the fog of war. Far from it; they knew all too well what was going on. They knew about the horror and the excessive violence; they knew civilians were being targeted; and they knew that the policy was doomed to failure. Their crime, and it was a crime, was to allow it to carry on.

“Alternatives were available," Greiner writes, and the decision-makers knew about them. They could have spoken out in favour of a different policy, with the support of "a substantial part of the political elite". One alternative would have been to secure a neutral, reunified Vietnam with communist participation in government. Indeed, that prospect was always on offer. So why did a succession of US presidents (with the diplomatic support, let us not forget, of their British allies) remain bogged down in a quagmire of their own creation? The question is still relevant today, as the protagonists in a similarly hopeless war in Afghanistan seek, and fail, to find a way to abandon a strategy that clearly has no hope of success.

Greiner's book is not a definitive history of the Vietnam war, but a well-documented essay on its violent, criminal reality and the failure of American society to come to terms with what happened. His implicit criticism of the role of the United States in Indochina, and his outright condemnation of US war crimes, derive from his distinctive perspective as a German historian. Inevitably, even though Greiner himself never spells this out, an uncomfortable comparison between US and Nazi war crimes grows in the reader's mind.

Only in an astonishing final section, where the author discusses the widespread American opposition to the trial of William Calley, does the shadow of Nuremberg flit across the pages. Lieutenant Calley was the officer held primarily responsible for the 1968 My Lai Massacre, in which 500 men, women and children were killed. The American public, across the political spectrum, objected to the way he was singled out for punishment, and the people rose up in their hundreds of thousands to support him. "Free Calley" was a slogan employed both by those hostile to the war and by those who would have liked it to be prosecuted more vigorously.

Although an account of My Lai makes up a central portion of War Without Fronts, the author argues that it was not exceptional: rape, torture and the murder of civilians had gone on before and continued afterwards. Greiner does not exonerate the murderers, the rapists and the practitioners of torture; but he also identifies the "real" war criminals - those who, from the top down, connived in allowing this to happen. He examines, in turn, the politicians, the generals, the officers and the soldiers themselves. They all knew what was going on, but could not find it in themselves to call a halt.

My Lai took place in March 1968, but did not become public knowledge until more than a year later, in November 1969, when the facts were laid out by the investigative journalist Seymour Hersh (the accurate details provided immediately after the event by Vietnamese insurgents were dismissed as propaganda). Yet concern about the nature and conduct of the war had been growing, particularly among veterans, for several years, and the then US defence secretary, Melvin Laird, became worried that My Lai would spark further revelations. He set up the Vietnam War Crimes Working Group to secure all information relating to US crimes during the occupation and to rebut the flow of accusations that was expected. In the process, says Greiner, the working group created "the most extensive archive about American war crimes", one barely touched by historians - until now.

Greiner's book concentrates on three episodes in the ground war in South Vietnam - the case of Task Force Oregon, which operated in 1967

in the five provinces immediately south of the border with North Vietnam; My Lai itself; and Operation Speedy Express, launched during the "pacification" of the five provinces south-west of Saigon in 1968-69. The details of these operations serve to bolster Greiner's contention that My Lai was no exception.

Task Force Oregon was given the job, in April 1967, of driving 300,000 people in Quang Ngai Province into "relocation centres". These were, in effect, prisons holding peasants loyal to the Vietcong. The province was then declared a "free fire zone", in which few prisoners were taken, troops were allowed to rape at will, and civilians were indiscriminately fired on. By the end of 1967, 70 per cent of the settlements of the province had been destroyed.

Much of this "calculated terrorism against civilians" was reported at the time by Jonathan Schell in the New Yorker, but even Schell didn't know that the Americans were also operating secret "Tiger Force" death squads, whose activities were fully uncovered only in 2003, thanks to the enterprise of two reporters from the Toledo Blade. Greiner describes how the death squads "shot peasants in the field without any pretext and murdered anyone who happened to cross their path; they tortured prisoners and executed them singly or in groups; they raided villages

in the late evening or early morning and mowed down with machine-gun fire everyone they could find - peasants who had gathered for

a meal or were sleeping, children playing in the open, old people taking a walk". They raped and murdered their victims and mutilated their bodies. Greiner notes that US customs officers came across dozens of parcels of human bones and skulls, often sent home to friends and relatives.

Operation Speedy Express was a repeat in the South of what had occurred in the North, with the additional use of helicopter gunships. Once again, civilians found themselves in an extensive "free fire zone" and helicopter crews embarked on indiscriminate killing of non-combatants.

My only regret is that Greiner deals solely with the activities of the US army. The equally heinous crimes of the US air force - the carpet-bombing of the North, the aerial destruction of Laos and Cambodia, and the bombardment by B-52s of selected areas of the South - are referred to, but left largely unexamined. During Operation Rolling Thunder, which lasted from 1965 until 1968, the four southern provinces of North Vietnam had more bombs dropped on them than any other area in history. When I travelled through North Vietnam during a halt in the bombing in the early weeks of 1970, I came across villages, towns, bridges, factories and railways that had been destroyed.

Two years later, in May 1972, President Nixon ordered the launching of Operation Linebacker, a six-month campaign that virtually destroyed the remaining industrial centres of the North. It was, writes Greiner, "the most massive attack in the history of aerial warfare". Designed to cover the withdrawal of front-line troops from the South, and to bolster the morale of the abandoned South Vietnamese army based in Saigon, it was perhaps the most cynical of the innumerable criminal acts of a filthy war.

“We're gonna level that goddam country," Nixon was recorded as saying in June 1971. "We're gonna hit 'em, bomb the livin' bejesus out of 'em." To which Henry Kissinger replied: "Mr President, I will enthusiastically support that, and I think it's the right thing to do." This served to prolong the war for several more years, until finally the Americans were ejected from the country they had tried to destroy.

Richard Gott's most recent book is “Hugo Chávez and the Bolivarian Revolution" (Verso, £9.99)