Congress MP Meenakshi Natarajan had complained in August last year that Singh had levelled "false, baseless and mendacious" allegations against Congress chief Sonia Gandhi for forcibly acquiring land from farmers of Haryana for Rajiv Gandhi Trust.
The matter was referred to the Privileges Committee of the Lok Sabha which is now considering.
During today's meeting of the Committee, clash between members of BJP and Congress took place when it was stated that Singh's allegations were "unsubstantiated" as the land belonged to a panchayat which willingly leased it to the trust.
A member said the trigger of the clash was the issue of calling Singh before the panel, which was opposed by BJP.
BJP members insisted that if Singh was called, then representatives of the trust should also be summoned.
The verbal duel involved Ananth Kumar and Shahnawaz Hussain of BJP and P S Bajwa, Arun Yadav and Anu Tandon of Congress.
The Committee will decide on the future course of action in the next meeting when its chairman P C Chacko moves a memorandum stating the findings and its decision.