Elliott Carter, the American composer whose kaleidoscopic, rigorously organized works established him as one of the most important and enduring voices in contemporary music, died on Monday in Manhattan. He was 103 and had continued to compose into his 11th decade, completing his last piece in August.

His death was announced by Virgil Blackwell, his personal assistant. Mr. Carter died in his Greenwich Village apartment, which he and his wife bought in 1945 and where he had lived ever since.

Mr. Carter’s music, which brought him dozens of awards, including two Pulitzer Prizes, could seem harmonically brash and melodically sharp-edged on the first hearing, but it often yielded drama and lyricism on better acquaintance. And though complexity and structural logic were hallmarks of his works, the music he composed in the decade leading up to his widely celebrated centenary, in 2008, was often more lyrical, if not necessarily softer at the edges.

Mr. Carter, a protégé of the American modernist Charles Ives, acknowledged that his works could seem incomprehensible to listeners who were not grounded in the developments of 20th-century music. Even trained musicians sometimes regarded his constructions as too difficult to grasp without intensive study. Yet he had many advocates among players, and his works were frequently performed and recorded.