The meeting at the CPI (M) office here was a "courtesy call," a TNCC release said.
Senior CPI (M) leader and former Rajya Sabha MP T K Rangarajan was also present during the meeting, it said.
After taking over as the President of TNCC, Elangovan had earlier called on DMK chief M Karunanidhi.
Elangovan was appointed as TNCC president following the resignation of B S Gnanadesikan who took sides with former Union Minister G K Vasan, who has announced to start his own party.