Dal Khalsa General Secretary Kanwarpal Singh said it was strange that the Deputy Chief Minister had recently announced that the case had been cracked and had even traced foreign links.
Police had arrested two brothers Rupinder Singh and Jaswinder Singh sometime back, with the state government claiming that they were responsible for the sacrilege and had committed the crime on orders of somebody in Australia.
United Akali Dal (UAD) convenor Mohkam Singh described the government's recommendation for CBI probe as a "clever ploy".
United Akali Dal and Dal Khalsa said the government step was part of "diversionary tactics to hoodwink the people".
Mohkam demanded immediate and unconditional release of Rupinder Singh and Jaswinder Singh, brothers from Panjgrain village in Moga arrested in connection with sacrilege incident at Bargari, the first to take place in the state.