NEW ORLEANS — Much of Leonard Cohen’s Thursday night concert at the Mahalia Jackson Theater had the reverent tone of a religious service. The reverence wasn’t directed toward a deity, however, but to music and to exquisitely shaped words expressed in song and to the unfathomable mysteries that accompany the human heart.

The gracious Cohen served as the evening’s minster of music. Wearing an elegantly simple dark suit and fedora, the 78-year-old singer-songwriter-poet often sank to his knees. Holding his microphone in his two hands, he looked like a man engaged in fervent prayer.

During “Ain’t No Cure for Love,” Cohen turned to his celestial trio of backup singers — Charley and Hattie Webb, aka the Webb Sisters, and his longtime collaborator, Sharon Robinson — and said, “Tell them, angels.”

Cohen’s songs, often but not always performed at stately, brooding tempos, do resemble prayers. “Bird on a Wire,” one his classics, has the gravitas of prayer, and Thursday’s performance of the song had the tone of a hymn. But Cohen being Cohen, the performance of “Amen,” from his 2012 album, “Old Ideas,” existed somewhere between a house of worship and a cabaret.

Cohen’s minimalist singing style is closer to speaking, or praying, than singing. Adding more weight to his lyrics and music, the years have deepened his voice from a soft baritone to a rumbling bass.

A sincere Cohen expressed his gratitude to his enraptured audience multiple times through his marathon concert.

“Thank you, friends, very much for your kindness,” he said early in a concert that began at 8:20 p.m. and ended far past 11 p.m. “I don’t know when we will meet again. No one ever knows that. But tonight I promise you, we will give you everything we’ve got.”

He kept the promise. Cohen and his amazing band, as well as Robinson and the Webb sisters, delivered exquisite performances of his classics as well as songs from the recent “Old Ideas.”

Cohen’s supporting players, including violinist Alexandru Bublichi and Javier Mas (a multi-instrumentalist who plays an arsenal of exotic stringed instruments), were perfectly attuned to his muse. The troupe’s synchronicity with its leader helped Cohen cast the evening’s hypnotic spell.

Frequently directing the audience’s attention away from himself, Cohen turned to his respective singers and musicians as they soloed, removing his hat and placing it over his heart. For a man of 78, too, he was quite spry, practically running on stage during his entrances and frequently dancing, albeit with economical movements.

Even though the concert’s first half was light on Cohen classics, it still was transporting. So, too, the second half.

Cohen stood in an ethereal spotlight as he sang another of his best-known songs, the haunting “Suzanne.” The song also was a rare instance of him accompanying himself with guitar.

The second half also saw him performing the best-known song in his catalog, “Hallelujah.” During the song’s chorus, lights turned upon the audience, as if Cohen was engaging his congregation in a mass embrace. “Hallelujah” received an especially moving performance within this extraordinarily engaging concert.