Gadkari, who was BJP's election in-charge for Delhi polls, accompanied Nigam to croon two lines of the famous song.
The 40-year-old Nigam seemed impressed by the vocal skills of Gadkari, who looked relaxed after his hectic campaigning in the lead up to the elections.
Nigam was in the city to attend 'Sonu Ki Sargam' during Agenda Aaj Tak conclave.
While the singer treated the audience with different songs, he sung 'Sandese Aate Hai' for Gadkari, who had reached before his own session, just to listen Nigam sing.
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The singer then sung 'Tujse Naraaz Nahi Zindegi' from 1983 film 'Masoom' and asked the BJP leader to join him.
Gadkari sung a few lines following which Nigam said, "He has a melodious voice."
Ghazal singers Talat Aziz and Pankaj Udhas also turned up for the session.