"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," the UN human rights office said in a statement.
The opposition-led National Assembly is organising a symbolic vote on embattled President Nicolas Maduro's bid to hold a July 30 election for a new assembly tasked with drafting a new constitution.
The opposition has staged waves of protests against Maduro, including a demonstration on Monday in Caracas during which dozens of protesters and some security force personnel confronting them were injured.
"It is vital that the government takes steps to ensure that the security forces... Do not use excessive force against demonstrators," the UN rights office said, adding that it had received reports of thousands of demonstrators being detained in previous rallies.
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With the crisis in Venezuela intensifying and Maduro under fire for what critics call his authoritarian moves, the UN refugee agency warned that the number of asylum applications from the country has soared.
"Last year, there were some 27,000 Venezuelan asylum seekers worldwide. So far in 2017, over 52,000 have applied for asylum," the UNHCR said in a statement.
The 52,000 figure represents "only a fraction of the total number of Venezuelans who may be in need of international protection," according to UNHCR.
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