"I have already informed the state Governor N N Vohra and the security agencies (about the threats). The calls were made from different Pakistani cities including Karachi, Rawalpandi and Muzaffarbad over the past couple of days," Mr Raina was quoted by news agency PTI.
Director General of State Police SP Vaid said no formal complaint has been received so far from the BJP president.
The BJP president said that he will not be "cowed down" by such threats. "What matters for me is my nation, my country, my motherland and the tricolour. I am a soldier of Bharat Mata and the BJP and will continue to work for the country and the state and will expose the nefarious designs of Pakistan."
The development comes days after the BJP pulled out of an alliance with the People's Democratic Party (PDP).
Mr Raina claimed that in one instance, a terrorist had called him and said he would meet the same fate as journalist Shujaat Bukhari, reported news agency ANI. Mr Bukhari (50), along with his two personal security guards, was shot dead by three motorcycle-borne assailants outside his office here on June 14.
"They are desperate and frustrated, they are making such ridiculous calls. We will never spare Pakistani 'wallas' (terrorists) and I challenge them and make it clear that they will not be spared and killed. Security forces have been given free hand (to deal with them)," he said.
"During the Ramzan ceasefire, it killed innocent people like journalist Shujat Bukhari in broad-day light and soldier Choudhary Aurangzab who was abducted and assassinated while going to his home to celebrate Eid," he said, adding earlier too many people like DSP Mohammad Ayoub was lynched on a holy night at Jamia Masjid in downtown Srinagar besides several other police officers and civilians.
He said he had exposed Pakistan and made it clear that it is an anti-Islamic country.
"Pakistan is a nation of coward people and I raised anti-Pakistan slogans in the state assembly. They are afraid of us," he said.
(with additional inputs from agencies)