When DMK member K S Ravichandran raised the issue of making Tamil the official language in the courts, Shanmugam said the Centre had assured the state government that it would present a proposal before the full bench of apex court, which had rejected a similar proposal in 2013.
"Reminders have been sent to the Central government," requesting it to place the proposal before the Supreme Court, he said.
The Minister meanwhile pointed out that arguments in many subordinate courts were being made in Tamil and in some cases, verdicts were also being delivered in Tamil.
Chief Minister J Jayalalithaa had also taken up the matter with Prime Minister Narendra Modi recently, he said.
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On the issue of providing security to the High Court, Shanmugam said CISF cover had been provided to Madras High Court as well as its Madurai bench in compliance with a Supreme Court order.
Shanmugam took a dig at the opposition party when he reminded them of a lawyers-police clash in the High Court campus in 2008 when even a judge was injured in the melee.
DMK was ruling the state then.
Insisting that law and order is being properly maintained during AIADMK rule, he said that this was "visible" during the recent "big level" advocates' protest last week, when they tried to lay siege of the High Court here, demanding withdrawal of new disciplinary rules.
DMK member Dravidamani urged the government to intervene in the issue to find an amicable solution.
Shanmugam said the High court had constituted a committee where lawyers could air their grievances on the new disciplinary rules.
The next meeting of the panel will be held this month, he said.