The remark by the five-time Lok Sabha MP from Karnataka that comes months ahead of the Assembly elections in the southern state sparked condemnation from Chief Minister Siddaramaiah who on Monday said the BJP leader does not know the parliamentary or political language.
Hegde, 49, said a new tradition was in vogue, where people project themselves as secular, but asserted he would feel "happy" if someone claims with pride that he is a Muslim, or a Christian, or a Lingayat, or a Brahmin, or a Hindu.
"I feel happy because he (the person) knows about his blood, but I don't know what to call those who claim themselves secular," said the minister for skill development and entrepreneurship.
"Those who, without knowing about their parental blood, call themselves secular, they don't have their own identity... They don't know about their parentage, but they are intellectuals," he said at an event organised by the Brahman Yuva Parishad in Kukanur town in Koppal district on Sunday.
He launched the Parishad's website and women's wing on Sunday.
Urging people to identify with their religion or caste, Hegde said, "I will bow to you, you are aware of your blood. But if you claim to be secular, there arises a doubt about who you are."
He said he respects the Constitution but "it will be changed in the days to come".
"We are here for that and that is why we have come."
Hitting out at Hegde, Siddaramaiah said the minister has not studied the Constitution, does not know the parliamentary or political language.
He said Hegde has not learned the social system and added that people belonging to various religions live in India.
"Each and every individual in this country is an Indian, and every religion has equal right and opportunity. He does not have this basic knowledge," Siddaramaiah told reporters in Hubballi.
Hegde is no stranger to controversies. A case was recently registered against him for allegedly using derogatory language against Siddaramaiah at Kittur in Belagavi district.
He had been slapped with cases for his "hate speeches", including one where he allegedly equated Islam with terrorism.
Commenting on the Tipu Sultan Jayanti controversy in Karnataka, Hegde was also quoted as having said at a public meeting that it is a matter of time before Chief Minister Siddaramaiah starts making people celebrate "Kasab Jayanti."
Ajmal Kasab was the lone surviving gunman from the coordinated terrorist attacks in Mumbai in 2008 that left 166 people dead. Kasab was hanged four years later.
Hegde was criticising Siddaramaiah for state-wide celebrations to mark Tipu Sultans birth anniversary on November 10.
The union minister was known to be vehemently opposed to the state celebrations of Tipu Jayanti since it was started in 2015 and had called the festival a "shameful event glorifying a brutal killer.