"The veil of secularism is much better than their (BJP's) communalism. Communalism divides the country," Congress general secretary Shakeel Ahmad said on micro-blogging site Twitter.
Earlier, speaking at a public meeting in Pune, Modi had charged that the Congress wears the veil of secularism and hides in a bunker each time it faces a crisis.
The BJP leader had alleged that the Congress uses this issue of secularism when asked about challenges like price rise, corruption and other issues.