Speaking in Madrid during a visit to Spain, Kuczynski said Venezuela's months-long political and economic crisis, which has seen thousands march for and against the government of leftist President Nicolas Maduro, could force people to leave the country in droves.
"If nothing is done, it will end in a blood bath, there will be a (migratory) invasion in Cucuta", in Colombia, Kuczynski said at a gathering organised by leading Spanish daily El Pais.
Kuczynski added that Venezuelans could also start crossing over to the Dutch island of Curacao north of their country in boats.
More than 60 people have been killed and hundreds more arrested during months of violent clashes in Venezuela.
The Peruvian president, a sharp critic of the current regime in Venezuela, has called for forming an international commission to try and resolve the crisis.
"Two or three democratic countries" could join several other allies of Venezuela as part of the commission, Kuczynski suggested, judging that all other attempts at easing the situation through multilateral organisations have failed.
Kuczynski made his comments following talks with Spanish Prime Minister Mariano Rajoy.
Kuczynski is in the country to drum up investments from Spain, which is Peru's biggest foreign investor, primarily in the energy, financial and telecommunications sectors, according to official Spanish data.
Eyewitness? Submit your stories now via social or:
Email: news@pulselive.co.ke
