The United Nation said the Venezuelan government should allow people to vote in the unofficial referendum on the constitution as the number of applications for asylum have soared.
The United Nations called on Venezuela's government to let people take part in an unofficial referendum on the constitution on Sunday and to make sure security forces do not use excessive force against protesters.
Opposition groups have called the plebiscite after months of protests, saying Venezuelans should have their say on President Nicolas Maduro's plan to rewrite the constitution.
The UN human rights office said six to eight million people were expected to take part.
"We urge authorities to respect the wishes of those who want to participate in this consultation and to guarantee people's rights to freedom of expression, association and peaceful assembly," UN human rights spokeswoman Liz Throssell said.
Hundreds of thousands of people have taken to the streets in Venezuela in recent months calling for an end to Maduro's presidency, amid food shortages, a collapsing currency and soaring inflation.
About 100 people have died and more than 1,500 have been injured in the anti-government unrest, which started in April.
The UN special rapporteur on freedom of assembly, Annalisa Ciampi, said she was deeply concerned about the pattern of violence by the police and National Guard, as well as reported attacks on voting centres by armed pro-government civilians.
"The Venezuelan authorities should not interfere with peaceful demonstrations, and indeed are obliged to actively protect assemblies," Ciampi said in a statement.
Thousands of demonstrators are reported to have been "arbitrarily detained" and more than 450 civilians are believed to have been brought before military tribunals, Throssell said.
Maduro is seeking to create a new super body called a Constituent Assembly, which would have powers to rewrite the constitution and dismiss the current opposition-controlled legislature, via a July 30 vote.
His opponents have accused the Socialist leader of economic incompetence, while Maduro says pro-opposition businessmen and the United States are waging an "economic war" against him.
Applications for asylum lodged by Venezuelan nationals have "soared," with 52,000 already this year against 27,000 in all of 2016, the UN refugee agency said. This represented "only a fraction" of those in need of safe harbour from violence and food shortages, it said.
Venezuelans have sought asylum mainly in the United States, Brazil, Argentina, Spain, Uruguay, and Mexico, UNHCR spokesman William Spindler said.
"UNHCR reiterates its call to states to protect the rights of Venezuelans, particularly the right to seek asylum and to have access to fair and effective asylum procedures," he said.
"Venezuelans should not be sent back against their will."