Responding to queries from reporters, External Affairs Ministry spokesperson Syed Akbaruddin said Azhar was the leader of a terrorist organisation which was not only banned by India but by the US and Pakistan.
"The concern for us is that a terrorist who is banned is able to spew venom on India," he said.
Azhar is said to be the brain behind the 2001 attack on the Indian parliament that almost caused a war between India and Pakistan.
A Pakistan newspaper had reported earlier this month that Azhar had addressed a rally over telephone in Muzaffarabad in Pakistani-held Kashmir, saying the first public appearance of sorts in years by the leader of an outlawed organisation had raised questions about the state's policy towards militancy.
The rally was held to launch a book apparently written by Afzal Guru, the Indian who was hanged after being convicted for the parliament attack.
Masood Azhar formed the JeM after his release by Indian authorities in exchange for the passengers of a hijacked Indian Airline plane in December 1999.
The organisation was banned by Pervez Musharraf's military government after the parliament attack, and splintered into several factions.
But despite the ban, Masood Azhar was never detained.