The party also announced a nation-wide protest on January 24 against Shinde's remarks.
BJP Chief Spokesperson Ravi Shankar Prasad said, "Sushilkumar Shinde must be sacked and the Prime Minister and Sonia Gandhi must tender an unconditional apology."
"BJP will not tolerate this repeated insult of Hindu and saffron traditions of India," he said, adding the party has never linked religion with terror as terrorists have no religion.
Terming Shinde has a "lightweight" Home Minister, Prasad said "he is a lightweight Home minister and is in the habit of speaking lightly. I condemn it strongly, very forcefully.
It is a malicious, baseless comment made by a lightweight Home Minister who doesn't know what he is speaking about."
BJP also said the Home Minister's comments will also help Pakistan which has always been in denial mode about flow of terrorism from its territory.
Questioning the Home Minister's intentions behind his comments of linking terror to Hindu organisations, the BJP leader said "saffron is the beacon of India's spiritual and religious heritage and holds a lot of importance in the independence of this country as saffron is also depicted on India's national flag.
"It is downright insult of India's spiritual, religious, cultural and civilisational heritage," he said, questioning if Sonia Gandhi is she approved of Shinde's remarks.
Prasad said why under Gandhi's stewardship the UPA government was "playing a joke with the feelings of Hindus".
"Why this is happening in your government, you being the senior-most leader of the party in power in the country? What is your reaction now? Does Congress approve of it?," he said.