Mr Rao made the controversial remarks at a candle march organised by the Karnataka Pradesh Congress in Bengaluru to show solidarity with the victims of rape in Uttar Pradesh's Unnao and Jammu and Kashmir's Kathua.
The comments drew an angry response from the BJP which termed them "heinous" and accused the ruling Congress of instigating violence.
As his comments stoked a major political row, Mr Rao said it was an "emotional outburst" and "all I said was just show him (Yogi Adityanath) slippers".
He said he regretted his remarks if they were offensive.
At the protest meet last night, Mr Rao had said, "This man from Uttar Pradesh who comes to Karnataka to deliver lectures is not a Yogi. He is a hypocrite, a liar and a thug. He should not be allowed to enter Karnataka..."
"... In case Yogi Adityanath No, there is no need to call him Yogi. He is Bhogi Adiyanath. If he comes to Karnataka, he should be beaten up with slippers and sent back. If you (Prime Minister Narendra Modi) have little self-esteem and if you have respect for women, sack the Uttar Pradesh chief minister. Unseat him. What you are doing now is a heinous crime (by retaining him)," he said.
Hitting back, furious Karnataka BJP leaders reminded Mr Rao that Mr Adityanath was a "revered saint of Nath tradition".
Strongly condemning the remarks, Karnataka BJP president BS Yeddyurappa said it was "highly derogatory and uncivilised".
He said a person who did not know how to speak about "a saint" and a democratically elected chief minister did not deserve to be in public life.
Mr Yeddyurappa asked Congress president Rahul Gandhi to expel Mr Rao from the party and said the Election Commission should also take cognisance of Mr Rao's "inflammatory remarks" and take "stern action" against him.
Vokkaligas are considered the second largest community in Karnataka after Lingayats.
The party termed it Congress "deep hatred" for saffron and anyone who is an "unapologetic Hindu".
"It also shows the party's disregard for rule of law," said the BJP, alleging, the "Congress instigates violence for political gain".
It asked the Election Commission to register a case against Mr Rao for promoting enmity between different groups under the Indian Penal Code.
The BJP said the statement shows Congress party's "utter contempt" for a democratically elected chief minister.
Enraged by Mr Rao's remarks, BJP MP from Mysuru Pratap Simha said in a video message, "One should be cautious while talking and control his tongue. Else, you will get a befitting reply."
Mr Rao said, "I should not have said so. It is wrong. All I said was just show him (Yogi Adityanath) slippers. I did not say slap him with slippers. It was not a scripted statement. In a fit of anger I said so. I was wrong."
Later, he tweeted, "It was an emotional outburst in a speech on the plight of the rape victims and the complete apathy of Adityanath government. I regret if it's offensive but the abuse of law in UP is a serious issue."