The Left party also urged all anti-BJP "secular" parties to come together on the issue.
"We are meeting government representatives today itself. They have not given any names but the anti-BJP parties require to unite for some secular, democratic candidate," CPI general secretary S Sudhakar Reddy said, while addressing the party's national council meeting here.
Reddy asked his partymen to take note of the BJP's victory in Uttar Pradesh Assembly elections, alleging that the party won by "dividing" people in the name of caste and religion.
Earlier today, the CPI(M) also pitched for fielding a candidate with "impeccable secular credentials" to be the next President.
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The three-day CPI meeting began with inaugural address by Reddy slamming the government over a wide variety of issues including death of farmers in police firing at Mandsaur, agricultural crisis, cow vigilantism and the latest notification of the government on cattle trade.
In several states, including Madhya Pradesh, Maharashtra, Punjab, Uttar Pradesh, there were good crops but prices have registered a sudden fall which is a serious concern, he said.
"In Madhya Pradesh's Mandsaur, it was pent up anger of the farmers as the BJP government failed to respond to their problems due to sharp fall in prices of their produce that led to killing of farmers," he said.
He also slammed BJP and alleged that cow vigilantism was being used to "terrorise" the Muslim minorities in the country.
"Cow has become a political weapon. The latest cattle notification is creating terror among the Muslim minority in the country."
The CPI veteran claimed that the effect of demonetisation on the economy was now visible with the slowing down of the GDP growth.
"The GDP growth rate has slid down to 6.1 per cent which is 1.4 per cent less than the expected growth rate. Demonetisation is going to have further adverse effects, including unemployment, in the coming days," he added.