Chief Metropolitan Magistrate Vishal Pahuja will consider the report to be submitted by the Delhi Police on February 11.
An inflammatory slogan "desh ke gaddaron ko goli maaro s*** ko" was chanted at a public rally addressed by Thakur on January 27 in Delhi's Rithala area. Thakur allegedly had egged on his audience to respond to the slogan.
Verma was reported as saying that mosques and graveyards had come up in over 500 government properties in the national capital, including hospitals and schools. He said that the land where these "illegal structures" have come up belong to the Delhi Development Authority, Municipal Corporations of Delhi, Delhi Jal Board and many other government agencies.
Thakur and Verma were then barred from campaigning by the Election Commission for 72 hours and 96 hours respectively in the run-up to the February 8 Delhi Assembly polls.
Karat filed the complaint against the duo on charges of outraging religious feelings, intending to provoke breach of trust and criminal intimidation.
"Direct that the investigation into the FIR be monitored by issuing necessary directions to the SHO concerned to investigate the matter fairly, properly and impartially, including arrest of the accused in accordance with the law," Karat said in her application.
The application was filed under Section 156 (3) of the Code of Criminal Procedure which empowers a magistrate to direct the police to conduct investigation into any matter.
( With inputs from IANS )