John Tavener opens his front door and his miniature dachshunds come flying out, yapping and wagging their tales as they scurry round my legs. "They were a great comfort to me when I was ill," he says. As we enter his Dorset home, his walking is laboured and his left hand permanently coiled. He is in constant pain, with shortness of breath and an abdominal complaint that is baffling his doctors. It's all in the wake of a series of heart attacks in 2007 that almost killed him. "They don't know what causes some of it. All they ever say is, 'You're lucky to be here at all!' Which is charming."

Soft light, dappled by the trees outside, fills this converted farmhouse as Tavener leads me into a rustic living room, and takes a seat on the well-loved sofa where he now composes (he's too frail to work in his study). His physical burdens seem to disappear the moment he starts talking about music, though: his face beams as he tells me about the epiphanies he had while listening to Mozart and Stravinsky at the age of 12. "They made me want to write music," he says. Recalling the works – Mozart's opera The Magic Flute and Stravinsky's choral-orchestral masterpiece, Canticum Sacrum – transports him back to his childhood, a place of energy and enthusiasm. "They are still guiding lights for me," he says. "They influenced the pieces that are being done in Manchester."

A major concert of new and rarely performed music by Tavener will take place at the Manchester international festival this weekend: three world premieres, with performers including tenor John Mark Ainsley, baritone Jonathan Lemalu, and cellist Steven Isserlis, his long-time collaborator and friend. "Canticum Sacrum is wonderfully archaic," he continues. "What Stravinsky does is extraordinary. It takes you on a journey from Gregorian chant right through to the modernism of Webern – and all in 17 minutes."

Tavener will be 70 next year. "If I make it," he says, and is promptly chided by his wife, Maryanna. But such gallows humour is perhaps unsurprising: for decades now, Tavener's radiant music has seemed to inhabit a place somewhere between this world and the next. His most famous pieces from the 1980s and 90s – slow, rapt, deceptively simple – have felt like attempts to glimpse eternity. The man himself has a similarly ethereal presence, with his shoulder-length hair, his height (6ft 6in), his thinness and frailness, and his aura of contemplation. But his eyes have a charm and an earthy twinkle that belies the mysticism.

The image of Tavener as musical mystic is partly down to the spiritual ideas – many drawn from ancient eastern traditions – that have fuelled his creative life. But it's an image that's far from the whole story. "The thing I regret most about my life are those inane photos of me with icons. They used to come down here and dress me up, and I just tolerated it. It's my fault. But I shouldn't have done it. They literally brought down costumes, candles and icons! It was unbelievable stupidity." Tavener means those many shots of him on album sleeves and in newspapers and magazines that were taken when The Protecting Veil, his part-serene, part-ecstatic cello concerto, became part of popular consciousness following Isserlis's unforgettable performance at the 1989 Proms.

While all that lazy visual symbolism helped turned Tavener into something of a spiritual superstar, it is a very superficial way of looking at the composer – and his music. The popularity of pieces such as 1982's The Lamb and 1993's Song for Athene (which was performed at Princess Diana's funeral in 1997) bemuses him. Both of these haunting choral miniatures were written as intimate works for family and friends; their global popularity is a remarkable but unintended consequence of their air of timelessness, their seeming simplicity. His phenomenal success – making him arguably the UK's most popular composer – led some critics to accuse Tavener of writing deliberately accessible music that tapped into a vague new-agey-ness for the most cynical of reasons.

This couldn't have been further from the truth. Tavener's shift away from the modernism of his youth to more spiritual sources – from the Russian Orthodox church to Hindu philosophers, from Gregorian chant to eastern musical ideas – is something that, he says, "almost paralysed me. But I don't apologise for the enthusiasm I felt. For example, when I said that my piece The Beautiful Names [a setting of the 99 names of Allah in the Koran] felt like a portrait of God, I meant it. That's how it felt to me when the music overcame me. I composed almost daily and I used to meditate – well, I walked round the garden rather than actually sat and meditated. I'd say the Arabic words, and then usually a melody would come to me." Despite stories to the contrary (he has said all the major religions are "as senile as each other"), he still defines himself as Russian Orthodox, even if he doesn't regularly go to church.

John Tavener in 1970. Photograph: Eric Wadsworth

Tavener feels he is now entering a new musical phase. "I remember thinking last year at the time of writing The Death of Ivan Ilyich [a distillation of Tolstoy's novel and one of the new Manchester pieces] that nothing I write now seems to go beyond 20 minutes. My language seems to be coming out much more tersely, much more compressed. I think the days of seven-hour pieces are gone." By this, Tavener means works such as 2003's The Veil of the Temple, his gigantic, through-till-dawn musical vigil.

He connects that terseness with his current physical state and current musical passions, which are taking him by surprise. "Since I've been ill, late Beethoven, his last string quartets, suddenly move me deeply. I've never been able to get Beethoven before. I always found the sound he makes alienates me. But now it moves me profoundly. I've become much more tolerant of music in general – and I'm listening to new music again. My attitude to modernism has changed, too." He loves the late works of Elliott Carter, a composer whose craggy dissonances you might have thought as far from Tavener's soundworld as possible. But he talks of them as "aural revelations".

Tavener says The Death of Ivan Ilyich – for solo baritone, trombones, strings and timpani, as well as Isserlis's cello – is "like the language of late Stravinsky. It uses the idea of musical shorthand, like Stravinsky's The Flood and Requiem Canticles. It is quite shortwinded for me. I think that's because I have a lot of shortness of breath at the moment." Ivan Ilyich is a story, he says, about "pain and transcendence. Ivan's life is pretty wretched. He treated his wife and son appallingly, and he has this terrible pain the doctors can't diagnose. Gradually, he starts to review his life. As he does so, the pain starts to recede. Right on the last page, there's a moment of transcendence. He is shouting and screaming in agony – and suddenly it all goes, as he asks his wife to forgive him, and his little boy is holding his hand. It's a harrowing novel."

Health-wise, the similarities are striking. "Having this pain all the time after the last illness has made me realise it's part of one's existence. It's something one just has to go through and try to transcend." Tavener even says he is grateful for the experience, but it's still surprising that this apparently most serene of composers should choose a work that confronts pain and death in such a stark and uncompromising way.

Tolstoy left the world in an existential panic, saying: "One must speak out from the top of Golgotha and affirm the truth by suffering and, better yet, by death." That's a much more nihilistic approach than Tavener's consoling visions of eternity and the afterlife, surely? "Tolstoy's is a via negativa, certainly, but the poets who have attracted me have often been pretty bleak, like Akhmatova. I was recently moved to tears by the beautiful pain of Schoenberg's Second String Quartet. And I think suffering has got something to do with that. Suffering is a kind of ecstasy, in a way. Having pain all the time makes me terribly, terribly grateful for every moment I've got."