India and Pakistan have fought two wars over control of Kashmir, divided between them since 1947.
Sayeed advocated a dialogue with Pakistan to settle the dispute, and sought to promote trade and travel between the divided parts of the insurgency-plagued Himalayan region.
At the start of insurgency in the Indian portion of Kashmir in 1989, one of Sayeed's daughters was abducted by rebels.
She was later freed in exchange for the Indian government releasing five militants from prison.
Modi and his Pakistani counterpart, Nawaz Sharif, who met last month, are struggling to keep a high-level dialogue on track after a militant attack last weekend on an Indian air base near the border.
India says the attack was carried out by Kashmiri separatists operating from Pakistan.
Based on reporting by Reuters, AP, and dpa