Three videos are rocketing around the Internet in which men, suspected to be based in Canada, are seen giving threats to the chief minister and Congress MP Ravneet Singh Bittu.
He dismissed media reports that the Punjab government has sought Z-plus security from the Centre for him and Bittu, saying the state police was "more than capable of protecting the people, including Congress leaders".
Singh in a statement said he was more than ready to take on "such forces which are trying hard to disrupt peace and harmony in Punjab. I will do everything in my power to thwart their nefarious designs".
The chief minister said he and his government will not be cowed down by the threats from such "spineless people who do not have the courage to come to Punjab and openly confront him".
He said if pro-Khalistan elements came to Punjab, his government will "take suitable action to ensure that they do not get away with their cowardly threats and attempts to revive terrorism in the state".
The Punjab government will retaliate in a suitable manner to ensure that peace in the state is not disturbed at any cost, he said.
An official spokesperson in the Chief Minister's Office also said Singh was not going seek additional security in the wake of the threats.
The chief minister has clearly told his officials and colleagues in the government that there should be no move on their part to scale up his security cover, the spokesperson said.
He said that organisations like Sikhs for Justice, which was purportedly behind some of the videos doing the rounds on social media, "were being supported, overtly or covertly, by certain Indian-origin members of Canadian Parliament".
These elements were bringing a bad name to the NRI Sikh community and diluting the latter's contribution to the development and progress of those countries, including Canada, he added.