European figures on Monday hit out at what one senior EU figure called "unthinkable" levels of repression in Venezuela.
At least three people were killed Sunday in clashes between protesters and police as voting proceeded on a controversial new 545-member Constitutional Assembly.
President Nicolas Maduro later claimed victory in the contest, but is facing some stern international criticism.
European Parliament President Antonio Tajani described the election as "a sad day for democracy in Venezuela, in Latin America and in the world as international treaties and the country's own constitution are violated, most importantly, against the will of the people".
Following a phone call with opposition leader Leopoldo Lopez, Tajani added: "In the last 24 hours chavist repression has reached unthinkable levels.
"The international community cannot remain silent in front of so many deaths in Venezuela. The press was not allowed to cover and report from polling places, this again demonstrates how undemocratic the current regime is."
Opposition leaders had called for a boycott of the election, fearing the new body would have powers to rewrite the constitution and dissolve state institutions.
The government wanted to avoid high abstention after 7.6 million voters two weeks ago cast ballots against the new assembly project in a symbolic referendum.
However, the European Commission said the new assembly had been "elected under doubtful and often violent circumstances" and could not be part of the solution to divisions in Venezuela.
"It has increased division and will further de-legitimize Venezuela's democratically elected institutions," the commission said in a statement.
Elsewhere, U.K. Foreign Secretary Boris Johnson said Venezuela stood on "the brink of disaster".
"The country is turning on itself -- more than 100 have died already -- and democracy and basic rights are in jeopardy.
"The dubious Constituent Assembly vote has dramatically deepened the problems and ramped up tensions."
Neighboring Colombia, Panama and Peru announced they would ignore the results.
Maduro went forward with the vote despite four months of protests by the opposition that left at least 116 dead, and pressure from the U.S., EU and several Latin America countries.
