Mahajan has called leaders of various parties for discussions over dinner. The winter session of Parliament, which has a huge legislative agenda, is scheduled to end on December 23.
Parliamentary Affairs Minister M Venkaiah Naidu has already said that government will go the extra mile to accomodate the opposition on debates on different issues.
Government managers hope that opposition will extend its cooperation to make the session a "more meaningful and constructive" affair.
The absence of Sonia Gandhi and Manmohan Singh during the expansion of the Union Ministry two weeks back is being seen as a pointer in this regard.
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Congress has been denied the Leader of the Opposition status in the Lok Sabha on the contention that its numbers 44 were less than one tenth strength of the House.
The session is also being held at a time when leaders of various political parties belonging to the 'Janata Parivar' are talking about joint floor management strategy and also for exploring a joint front against a resurgent BJP.
In the session, government plans to pass most of the old pending bills as well as some key new bills.
The BJP-led NDA does not have a majority in the Rajya Sabha and will have to depend upon the cooperation of the Opposition to get key bills passed.