His appeal came as the Supreme Court was all set to deliver its judgement in the Ram Janmabhoomi-Babri Masjid title dispute case.
In a statement issued here, Palaniswami said the Tamil Nadu government is maintaining religious peace in the state and the Ayodhya case is set for final decision by the apex court after crossing several stages.
Palaniswami said all the parties should respect the Supreme Court judgement and maintain calm and peace without giving space to any law and order problem.
The Tamil Nadu Muslim Munnetra Kazhagam (TNMMK) has also appealed to maintain peace whichever way the Supreme Court judgement goes.
The President of TNMMK (TNMMK) M. H. Jawahirullah said the Muslim community has confidence in law and the apex court, and expects the judgement would strengthen this belief.
Meanwhile, security across the state has been beefed up with armed police being posted as a precautionary step near all the places of worship.
According to the police, about 15,000 security personnel have been deployed in the city.
Similarly places like commercial complexes and others where large number of people congregate have been put under strict watch.
The police is also keeping a watch on the important temples across the state.
Security has been strengthened around nuclear power plant in Kudankulam, Indian Space Research Organisation's (ISRO) Liquid Propulsion Systems Centre in Mahendragiri and V.O. Chidambaranar Port in Thoothukudi.
( With inputs from IANS )