A series of blasts had taken place at the rally site claiming six lives.
"Police officials came to me and said don't address the public meeting as some blasts have taken place. They said the same thing to Narendra Modi. I said no, whatever happnes, we will address the rally. If we had cancelled the rally, then there would have been riots and violence in the whole of Bihar," Singh said in an interview to India TV.
Asked about the charge that BJP leaders were playing politics by visiting families of the victims and offering Rs 5 lakh compensation, Singh said "they were our workers, our well-wishers. This should not be seen as taking political advantage. Had there been communal clashes, you could have said that we took political advantage."
The BJP chief denied reports that his party had demanded SPG cover for Modi after the blasts.
Singh refuted claims by some sections that BJP will face losses by projecting Harsh Vardhan as its Chief Ministerial candidate in Delhi.