In the first week of his presidency, Barack Obama received about 250,000 letters from ordinary Americans. Over the course of the following eight years, the number settled at roughly 10,000 a day. Most of his correspondents had heard that he was in the habit, from his days as senator, and on the campaign trail, of trying to reply to letter writers with a handwritten note. Obviously, the change in scale and responsibility meant that task was impossible to fulfil comprehensively; instead, Obama committed himself to answering 10 letters each day. These were selected by a small and dedicated group of readers in a specially convened mail room; they called themselves “Team Little People”, and they operated with a kind of messianic devotion to the task of sifting and sorting, putting forward a range of letters – both supportive and antagonistic – that appeared to come most closely from the heart.

Jeanne Marie Laskas first gained access to the White House’s epistolary army for an article in the New York Times – an article that Obama described as the “single favourite story of my presidency”. Laskas expands it to book length here with singular chapters about some of the individuals Obama chose to correspond with, as well as copious reproductions of the letters involved. It makes a moving and inevitably nostalgic or even elegiac read, redolent of the human grace and statesmanship of the Obama presidency, qualities so brutally absent in the current administration.

Obama liked to save the purple folder in which the 10 selected letters appeared until the end of his working day, after having had dinner with his family and read two or three hours of briefing papers and security reports. Having used the letters while campaigning to shape the story he was telling on the stump, to “orient himself”, in power he came to see them as a valuable reminder of service. “It was a way for me to, every day, remember that what I was doing was not about me,” he observes here, totells the author, in one of a couple of long interviews. “It wasn’t about the Washington calculus … It was about the people who were out there living their lives, who were either looking for some help or angry about how I was screwing something up.”

The letters came from military veterans and the parents of those who had been victims of gun crime. They came from schoolchildren asking the president to assess their homework and single mums trying to pay the rent. They came from millionaires and bankrupts, from professors and prison inmates. Some had a direct poetry or heartfelt candour, like that from Bobby Ingram, of Oxford, Mississippi, who described how he missed the worker’s calluses on his hands after losing the job he’d had for 23 years as a land surveyor: “I kneel nights and clutch new hands together, praying we can all recover what seems lost.” Others, like that from Ronn Ohl, a Tea Party conservative from Washington DC, came with several paragraphs of pointed criticism of Obama’s perceived liberalism, before confessing a grudging epiphany over the president’s Dream Act, his proposal of amnesty for the children of illegal immigrants, an initiative that had enabled a young Hispanic man known to the letter writer to become a productive citizen.

There are letters of hardships and illnesses overcome, and those that tell of long lives with no happy ending, stories of modern America in a side of handwritten foolscap. Quite a few are powerfully moving in their hope, as well as their desperation. Some, most of which never reached the president, were given a “red dot” by the mail-room team. These were considered emergencies: letters from people who expressed a desire to kill themselves or someone else. About 200 letters a day were red-dotted, their senders immediately contacted.

Sometimes, Obama confesses, he felt that he was devoting more time and effort and attention to his late-night replies than the task required; he did so, he explains, “because he really wanted people to know that this isn’t just the comments on the internet. That’s not the function of this. The function is: ‘We’re going to engage’”. The tone and courtesy of that engagement – the president clearly made sure he read between the lines of the chosen letters, and found ways to establish careful empathy – stands as a beacon of humble leadership, as does the dedication that Obama inspired in the mail-room team that made the correspondence possible.

There will be those, of course, who read or respond to the idea of Laskas’s beautifully researched and written book with the argument that the 44th president was all about this vaunted compassion, about always having the right words, but not always having the right deeds. There are plenty of ways to counter that argument, but one is that writing a letter is itself a deed, an action, requiring a degree of dedication and thought, a capacity to listen, in the way that firing off an exclamatory tweet never is.

• To Obama With Love, Joy, Hate and Despair by Jeanne Marie Laskas is published by Bloomsbury (£20). To order a copy for £17.20 go to guardianbookshop.com or call 0330 333 6846. Free UK p&p over £10, online orders only. Phone orders min p&p of £1.99