Lal Krishna Advani and other Hindu hardliners are accused of inciting thousands of Hindu zealots to pull down the 16th century Babri mosque in 1992.
They said the mosque was built after a temple to their mythological warrior god Ram was destroyed.
The court issued notices on Monday to Advani, Human Resources Development Minister Murli Manohar Joshi, and federal detectives asking why they had sought to drop conspiracy charges in the case.
The demolition sparked off nationwide Hindu-Muslims riots that left 2000 people dead.
It became a key issue in the electoral campaign of the Hindu nationalist BJP party, which now heads the coalition government.
In May detectives of the Central Bureau of Investigation (CBI) filed a formal petition seeking to quash conspiracy charges against the deputy prime minister.
The Babri mosque was demolished
by Hindu hardliners in 1992
Last month, Prime Minister Atal Behari Vajpayee rejected opposition charges the CBI had been "used" to protect Advani and the others.
The dispute over the site is now in the hands of the courts, which ordered experts of the Archaeological Survey of India (ASI) to excavate the site.
A summary of a report submitted to the court last week described a 10th-century temple with Hindu carvings under the rubble of the Babri mosque.
However, the ASI had made no mention of the Hindu carvings in a preliminary report.