It said the rejection was handed first in Delhi now Bihar.
Congratulating JD(U) leader Nitish Kumar and RJD chief Lalu Prasad following the grand alliance's victory in the Assembly polls, the Left parties stressed, the struggle for "better India" intensifies from here on.
On the performance of Left Front, CPI maintained the results were "not encouraging".
The CPI (ML), however, expressed satisfaction that amid the faceoff between the NDA and JD(U)-RJD-Congress combine, it managed to win two seats and was in close contest in two more constituencies where counting was still on.
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His party colleague and Rajya Sabha member, D Raja, echoed similar views and termed JD(U)-RJD-Congress grand alliance' victory as "decisive".
CPI (M) general secretary Sitaram Yechury observed the verdict ensured beginning of "good days" for people as they rejected alleged communal polarisation by RSS-BJP and its "so-called" development agenda.
"People's acche din have begun, first Delhi, yesterday Kerala and today Bihar.
The subtext of the verdict is very clear that is people have rejected the communal polarisation that was going on by the RSS and BJP and rejected the claims of so-called development agenda of the government," Yechury said
"Nitish ji, Congratulations, well done. Now, for bigger battles. Lalu ji, Congratulations. Ek behtar Bharat ke liye, ab sangharsh tez hoga," he said in series of tweets.
In a statement issued later, the CPI (M) congratulated people of Bihar for giving a "resounding" defeat to BJP alliance by rejecting the rank communal campaign conducted by the BJP, led by the Narendra Modi-Amit Shah duo with "divisive" issues like cow and beef and the bogey of reservations for minorities.