The Congress has denied the report, published recently in an Urdu daily, as false and baseless.
Addressing a press conference at the BJP headquarters, senior leader Prakash Javadekar questioned the Congress president's silence over the issue and said he should come out in the open and clear his stand.
The Congress, he said, stands exposed by its president's statement.
"It is a communal party. Its appeasement politics have damaged the country. The history of partition is testimony to this," Javadekar told reporters.
Javadekar, who is also Union HRD minister, said such remarks by a national party chief cannot be ignored and added that similar statements had been made by other Congress leaders as well.
He accused the Congress of having a "divisive ideology", and referred to the anti-Sikh violence in 1984 when thousands of Sikhs were killed following the assassination of Indira Gandhi as the "only genocide" India had witnessed.
He also referred to the controversial Shah Bano case during Rajiv Gandhi's tenure as prime minister. To forward its appeasement politics, he said, the Congress-led government had even changed the country's constitution.
In 1985, Shah Bano, a 62-year-old woman, was granted maintenance from her ex-husband by the Supreme Court. The judgement was reversed due to religious and political pressure after which the then Congress government passed the Muslim Women (Protection of Rights on Divorce) Act which diluted the verdict.
Javadekar also referred to Congress leader Manmohan Singh's remarks when he was prime minister that Muslims have first right over resources of the country.
The BJP leader claimed the Congress' minority cell president Nadeem Javed had justified Gandhi's remark and asserted he was right in saying that Congress is a Muslim party.
The BJP leader also questioned why Gandhi had not spoken about the practice of triple talaq, and asked whether the opposition party had place only for Muslim men and not women, echoing Prime Minister Narendra Modi's speech in Azamgarh over the weekend.
The Monsoon Session of Parliament is set to begin on Wednesday with the triple talaq bill topping the government's agenda.
Yesterday, Union Minister Ravi Shanker Prasad had asked Gandhi to break his silence on the Muslim party remark.
When Gandhi goes to Gujarat for elections, he becomes a 'janeudhari' (one who wears the sacred thread) and flaunts his Brahmin lineage. He does the same in Karnataka. Now when the elections are over, he starts patronising the Muslims, Prasad said.