Representatives of the two parties made the plea before the full Election Commission, headed by Chief Election Commissioner V S Sampath, here during a hearing.
The EC had issued notices to BSP, NCP and CPI asking them why their national party status should not be withdrawn following their performance in the Lok Sabha elections.
In the Lok Sabha polls, BSP did not win any seat while CPI managed only one. NCP also managed only six seats.
The EC had called Sharad Pawar's NCP, CPI and BSP for a personal hearing as their recognition is under review following their failure to fulfill the conditions for retaining recognition as national parties.
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CPI's D Raja, while appearing for the party, admitted that its performance in the Lok Sabha polls was not according to expectation.
Raja said he urged the poll panel not to take a decision on the issue till the assembly elections in Jammu and Kashmir, Jharkhand, Maharashtra and Haryana are over.
NCP leader Praful Patel, who appeared for his party, insisted that it already fulfills the criteria. At the same time, he urged the EC to wait for the results of the assembly polls.
"Yes, we also said that EC should wait till the outcome of assembly polls. There can be change after every poll," Patel told PTI.
Besides the three, Congress, CPI-M and BJP are the other three 'national parties'.