The meeting was attended by party General Secretary Prakash Karat and senior leaders like Sitaram Yechury, Biman Bose, Brinda Karat and others.
Sources said one section of the party is for abstaining from the poll while another is for supporting Mukherjee.
The section advocating abstention is of the view that they cannot be seen voting for a Congress candidate. The meeting comes ahead of the Left party meeting here to finalise its strategy on the issue.
Mukherjee has reached out to Karat seeking his party`s support but did not get any commitment. Mukherjee telephoned Karat yesterday as part of the exercise to get support from non-UPA parties.
Sources said Karat was non-committal and told him that CPI-M Polit Bureau was meeting tomorrow followed by a meeting of Left parties where a decision on the issue will be taken.
Left parties account for around 51,000 vote value in the electoral college of 10.98 lakh vote value and Mukherjee has already garnered support of parties which has a total vote value of 5.44 lakh. If all the votes are polled and counted valid, then the winning candidate needs to get atleast 5,49,442 votes.
The Left parties have kept a suspense on the issue of support to the UPA nominee, saying they were not bound to back the ruling coalition`s candidate. "We are not bound, we are not part of the alliance of Congress and UPA that we have to support anybody they propose," Karat had said.
The CPI-M had earlier decided to consult secular and Left parties before finalising a stand on supporting a Presidential candidate.
The Presidential poll, slated next month, was also discussed in the recent CPI-M Central Committee meeting, which authorised the Polit Bureau to formulate the party`s strategy on the election after discussing the issue with other Left and like-minded secular parties.