Lawyers belonging to various associations, including the Madras High Court Advocates Association, commenced the fast on Monday morning.
MHAA secretary M Velmurugan said the future course of action would be decided at the end of the fast on Monday evening.
Meanwhile, courts all over Tamil Nadu remained closed Monday as per the order of the high court to keep them shut till Tuesday to enable restoration of normalcy.
Hardening their stand, various associations of the lawyers on Sunday had decided to boycott the courts indefinitely and sought the removal of the state Director General of Police and the Chennai city commissioner in connection with the violence in the court complex.
They had also sought deployment of central security forces in the high court complex.
Chief Minister M Karunanidhi, convalescing in a hospital after a spine surgery, had said on Sunday night that he would go on a fast if the police and lawyers failed to find an amicable solution to end the standoff.