The Seagram Building was to be the epitome of style, grace and modernity in New York in the late 1950s. Inside Mies van der Rohe’s great glass tower, everything had to be the best of the best. The finest travertine marble, the most perfectly brushed stainless steel, the most achingly understated furniture – all these could be sourced, albeit at a cost. But when architects Philip Johnson and Phyllis Lambert, herself an heiress to the Seagram fortune, were entrusted with the design of the new Four Seasons Restaurant on the ground floor, they had a dilemma. Which modern painter should they approach to paint the decorations?

They consulted Alfred Barr, Director of the Museum of Modern Art and principal arbiter of taste in New York at the time. It was 1958, the same year in which Mark Rothko had been selected to represent America at the Venice Biennale with a series of broodingly monumental paintings – pictures which, with their tripartite fields of dark and vibrant reds and blacks, had spurred critics to coin the new term “abstract sublime”. Rothko was Barr’s unequivocal choice. Johnson and Lambert approached the artist, who immediately agreed to furnish the required paintings. So began the most famously misconceived commission in the history of modern American painting – which is now the subject of a subtle, poignant and deeply moving new exhibition at Tate Modern.

Mark Rothko, who had been born in Dvinsk, Russia, in 1903, was an agnostic Jewish immigrant American who yearned to invest the language of what had become known as Abstract Expressionism with the spiritual power of the greatest religious art of old Catholic Europe. He believed that pure colour, laid on to the canvas in translucent layers and fields, could be used to express “basic human emotions – tragedy, ecstasy, doom.” Even in a secular age, he argued, art could still engender profound spiritual experiences. “The people who weep before my pictures are having the same religious experience I had when I painted them.” That was Rothko at his most strident. But he was capable of doubt and ambivalence too, emotions reflected in the quotation that serves as frontispiece to the catalogue of Tate Modern’s new show: “If people want sacred experiences they will find them here. If they want profane experiences they’ll find them too. I take no sides.”

To make sense of the exhibition, which brings together some 50 majestic late works by Rothko, it is necessary to know something of the tortuous history of the Seagram murals commission. Having agreed to paint the pictures for the Four Seasons restaurant, the artist immediately found a vast new studio in a former YMCA basketball court in Manhattan. He was planning to work on a larger scale than ever before. The works that he had in mind were to be conceived as a series, so he needed to be able to see how they fitted together. His health was poor, because like most of his fellow Abstract Expressionists, he subscribed to a Hemingway-esque macho cult of creative self-destructiveness (there is hardly a photograph of Rothko in his maturity in which he is not to be seen smoking a cigarette). But he worked with a fury, nonetheless, completing approximately thirty works – far more than strictly necessary – between the autumn of 1958 and the summer of 1959. Inspired by the accidental sight of one of his characteristic, vertically oriented abstractions lying on its side in his studio, he switched to long, low horizontal formats and square paintings – pictures that looked a little like blank doors and windows.

All the time, he had nagging doubts about the wisdom of committing the works to a restaurant frequented by the well-heeled from Wall Street. Despite the alacrity with which he had accepted the commission, it seems that he had always had his doubts about going through with it – boasting to friends about the get-out clause he had extracted from Johnson and Lambert, which allowed him to repay his fee in exchange for keeping the pictures, if he should so choose. That was indeed his decision, finally taken following an actual meal in the Four Seasons. He is said to have been repelled by the very luxury of the experience. In the end, Rothko ended up with three series of pictures, the majority of which are extremely dark works in maroon and black, with one or two exceptions executed in lighter tones and brighter, orange colours. The pick of the works, nine murals in total, were eventually given by the artist to the Tate. Another impressive group was given to the Kawamura Memorial Museum of Art in Japan, while the Metropolitan Museum, in New York, got the rest.

No fewer than fifteen of the Seagram mural paintings have been brought together in the broad and spacious gallery that forms the core of Tate Modern’s exhibition. To Tate’s own nine pictures have been added six more from the collections at Kawamura and Washington. They are dark, solemn, uncompromisingly ambitious paintings, alive with glows and glimmerings of oil paint applied so stealthily, in etherised washes and feather-edged brushstrokes, that it might almost be watercolour. There are intimations of light, foreclosed by surrounding darkness, that manage to suggest infinite depth and utter flatness at one and the same time.

This is the first time that a display attempting to recreate the full, serial effect of the works has been attempted. The paintings have been hung unusually high on the wall, as they would have been in the Four Seasons restaurant, above the diners seated at their tables. But this is also how Rothko looked at them himself, in his new Manhattan studio. The German art historian Werner Haftmann, who visited Rothko when he was at work on the series, has left a memorable description of the scene:

“At a certain height, there was a darkly luminous frieze of pictures running around the whole room... Rothko told me that he had regarded this commission as a great and wonderful task, and that here his work had reached a climax. In the zeal of his monologue, he did not hesitate to speak of ‘the Sistine Chapel’ ... Soon we were encompassed by these darkening walls of light. It was a very spiritual luminosity that emanated from these backgrounds. It was not a real light and did not suggest any perspective. It had no source ... Here and there, a dark curve indicated a kind of gate. But the gate did not open.”

The passage is sharply expressive of the author’s struggle to put such unfamiliar images – or absences of image – into words. It is, in fact, a very accurate description of the effects that the pictures have in the current display at Tate Modern (arranged with exemplary sensitivity and respect by the exhibition’s curator, Achim Borchardt Hume). It also suggests, very clearly, just why Rothko felt compelled to withdraw from his contract to deliver the paintings to the Four Seasons. He had accepted the commission with alacrity, not because of the prestige of the Seagram building, but because it offered him the opportunity to paint a series – to compete, as it were on his own terms, with the great serial masterpieces of past art such as Michelangelo’s great fresco cycle for the Sistine Chapel ceiling. Perhaps the idea of painting such a work for a restaurant struck him, initially, as not entirely inappropriate. After all, some of the greatest works of sacred art had been painted for places where men eat – Leonardo da Vinci’s Last Supper, for example, in the refectory of Santa Maria delle Grazie in Milan. But on reflection Rothko must have decided that a swish Manhattan eatery was insufficiently charged with spiritual seriousness for his purposes.

Rothko’s Seagram murals go to the centre of his paradoxical art and encapsulate the sense of crisis that was to engulf him during the last ten years of his life. If they resemble any work of Renaissance art it is not the paintings of the Sistine Chapel ceiling but – as Rothko himself said – the blind doors and windows of Michelangelo’s Laurentian Library staircase. Michelangelo’s blank forms were charged with optimistic Neoplatonic  symbolism. What they say, to those standing at the entrance to library, is that to remain outside is to remain blind, whereas to enter the world of knowledge and learning is to become enlightened. But such optimism was not a possibility for Rothko. His art speaks of spiritual yearning, certainly, but of a yearning that is tragically and constantly contradicted by the sense that, ultimately, transcendence is not possible. What might seem to be a window into infinite space is – as Haftmann says – a closed form like a barred gate.

The bleak context that has been given to the Seagram murals in Tate’s exhibition only serves to enhance their pathos. The works are exhibited alongside the last and darkest series of his paintings, the Black-Form paintings of the mid-1960s and the Black and Gray works of 1969-70. Consisting simply of upright canvases bisected by two planes – a lower field of grey surmounted by a field of subtly inflected blackness – these works picture the world as an empty, abandoned, desolate space. They bear an intriguing resemblance to the exactly contemporary works of Francis Bacon, whose current retrospective at Tate Britain fortuitously coincides with this show. But Rothko’s pictures give us Bacon’s disenchanted world purged to utter emptiness – unrelieved, even, by the Dionysian revels of human flesh.

The knowledge that Rothko committed suicide while working on the very last of these pictures should not completely condition response to their effects. The primary cause for the artist’s sense of despair was not existential anxiety but the knowledge that his health was so poor that death was imminent anyway. But his last works are, undeniably, as final and as bleak as any pictures painted in the second half of the twentieth century.