Suffering trauma, boredom and shame from covering over-optimistic US military involvements in Afghanistan and Iraq, American reporter Lisette Marigny whimsically asks a search engine: “Are there any wars right now that we’re not losing?” The algorithm claims the answer to be “Colombia”, where, in 2015, US troops are supporting a national rebuilding and peace process after half a century of intersecting civil wars between government forces, terrorists, revolutionaries and drug barons.

Lisette contrives an assignment there, intersecting with Major Mason Baumer, a Marine medic who, haunted by catastrophic casualties he saw in the same wars that unnerved the journalist, has taken what he hopes will be a more constructive posting as a special forces liaison officer at the Bogotá embassy.

Klay, a Marine veteran, wrote about men at war in his award-winning 2014 short story collection Redeployment, the awful authenticity of which is also evident in Missionaries, his debut novel. Many details feel memoir-real, either experienced or observed: a ruined school still bears a sign boasting that it was donated by the United Nations; a humanitarian group called Clowns Without Borders seeks to cheer up war-zone children. Phone calls from tours of duty are agonisingly stilted because military advice to service personnel is to say nothing of the conflict, while loved ones have been warned not to burden them with domestic dismay.

If the book were a movie, it would have an 18 certificate for the battlefield scenes alone. Enemy explosives and bullets, Mason tells us, often target the intestines because of the double indignity of a dying body losing blood and shit. Some guerrilla weapons contain chemicals mixed with faeces, so that burns or wounds become rapidly infected. This excretory imagery embodies the book’s depiction of humanity turned inside out in conflict.

While Mason’s experiences are close to what Klay has known and described in Redeployment, the novel also advances into more distant gender and geographical territory than his briefer fictions, presenting (mainly in the first person) the perspectives not only of Lisette, but Abel, a poor Venezuelan; Juan Pablo, a rich Colombian; and Diego, a Chilean mercenary. In the current debate over the scope and ownership of fiction, Missionaries makes a strong case for expansive imagination of other lives.

In this effort, Klay may have taken courage from his main fictional model. Identifying as a Catholic novelist, in writing fiction set in foreign war zones he makes a second genuflection to Graham Greene. Both Lisette and Mason fear, like Greene’s Querry in A Burnt-Out Case (1960), that they have lost the ability to feel, and must seek it in new experience, although Klay makes this torpor of the senses grimly broader. Lisette becomes convinced that her war reports have little impact in her homeland because “no matter how jaded I’ve become, I’ll never be as jaded as the average American”.

Missionaries also includes a character, rare outside Greene, who believes that humans bear the curse of “original sin”, while the writer of The Heart of the Matter might be tempted to the sin of envy by the doleful local atmospherics – “a city after a bombing is like coming upon the decayed body of an animal in the woods” – and would surely have loved a scene in which a character confesses to a priest all the people he has killed but is told that he is absolved by God because the brutality was done for his country.

Klay’s novel has the feel of a knowing coda to American fiction of the Vietnam war, such as Robert Stone’s Dog Soldiers (1974), Tim O’Brien’s The Things They Carried (1990), and Karl Marlantes’s Matterhorn (2010). In the book’s biggest US-set scene, Lisette visits her Uncle Carey, a Vietnam veteran who has never recovered from his missions there; we guess that his niece, in searching for a “good war”, is attempting to redeem both him and her nation.

But while the Americans in Missionaries want to be involved in a success story overseas, readers will bet that this dream will be hard to achieve. In a pivotal passage, Lisette reflects that all the US’s post-Vietnam military adventures – Iraq, Afghanistan, the Philippines, Colombia – are, in fact, “the same war … related to the demands of America’s not-quite empire”.

That is one of the places where the novel contains more insight into the theory and practice of war and politics than many hefty histories. Mason’s American creed that “you must accept that the true will of the people aligns with whatever the central government believes” is challenged by a South American reality in which ideological loyalties can be bewilderingly fractured.

The novel’s structure subtly reflects this: the perspective of the first section is divided between two characters; the second alternates a different pair; and the third, after a shocking thriller plot twist, shuffles the voices with desperate momentum. As the available storytellers are cruelly reduced, the choice of the last speaker feels true to the meaning of the story.

In an Afterword, Klay alludes to the difficulty in stretching from stories to novels. But this sweeping, searing, wrenching and wise addition to the great literature of America’s postwar imperialism ends absolutely as mission accomplished.

• Missionaries is published by Canongate (£16.99). To order a copy go to guardianbookshop.com. Delivery charges may apply.