"People say all kinds of things off the record. But if Sonia Gandhi and Rahul Gandhi were hurt by my remarks, then I apologise," he said.
Singh had said on Tuesday at Hajipur in Bihar that if Rajiv Gandhi had married a Nigerian lady and not a white-skinned woman, then Congress would not have accepted her leadership.
Reacting to his comment, the Congress said the minister's remarks were bordering on insanity.
"The comments reflect the lack of moral fibre in the BJP. It appears that the continuous quest to appease Prime Minister Narendra Modi has made him lose his balance," party spokesperson Randeep Singh Surjewala said.
"He is a serial offender. The PM has a duty to publicly correct this situation. What is the PM's Mann ki Baat on this? His silence reflects connivance and encouragement," said CPI(M) leader Brinda Karat said.
"It is shocking. The PM can't be expected to comment on each and everything but I am sure this is a matter of concern for the party," said former IPS officer and BJP leader Kiran Bedi.
Singh, who in the past made several other controversial remarks, however, had said he was only chatting informally after a press conference.
A BJP MP from Bihar's Nawada constituency, Singh made it to the Narendra Modi's council of ministers in November. He is a former Bihar minister in the cabinet of Nitish Kumar. He was among the eleven BJP ministers who were dismissed by Nitish Kumar as a result of breaking of JDU-BJP alliance.
Before last year's Lok Sabha election, he had said that critics of Narendra Modi should be sent to Pakistan.
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