"The rally addressed by Modi (Monday) had a portrait of Lord Ram as the backdrop. Modi also made a direct appeal invoking the name of Ram in his political statements," the CPI-M said in a statement.
"These are a blatant misuse of religious appeal for electoral purposes. The Election Commission should immediately take action against this electoral offence," it said.
The Communist Party of India-Marxist also accused Modi and BJP president Rajnath Singh of "constantly raising the issue of 'Bangladeshi' infiltrators in order to target the Bengali-speaking Muslims.
"In a number of speeches made in Assam and West Bengal, they have threatened that these 'infiltrators' will be thrown out of the country.
"Such a campaign with communal overtones has caused insecurity amongst minorities and raised tensions. This has been one of the factors that contributed to the killing of 31 people in the Bodoland Territorial District of Assam where Bengali-speaking Muslims were targeted by Bodo extremists," the CPI-M said.
The CPI-M condemned "this rabid communal propaganda by the BJP leadership" and urged the Election Commission to "immediately intervene to stop the BJP from indulging in such communal targeting".