The court also ordered allotment of five acres of land at an alternate site to the Muslims for building a mosque.
In a statement issued here DMK President M.K. Stalin said the apex court has found a solution for a long pending dispute.
Stalin said he believes that the judgement will be accepted by all and maintain communal harmony without and damage to the pluralistic society.
In a statement issued here on Saturday, the Indian Union of Muslim League (IUML) National President K.M. Kader Mohideen said there is no necessity now to deliberate on the pros and cons of the apex court's judgement.
He said the need of the hour is to respect and accept the court judgement and take steps to implement the same.
The Tamil Nadu Unit of Communist Party of India (CPI) urged all to respect the apex court's decision and maintain peace.