The vote is being boycotted by the opposition, which says the election is fraudulent and created to secure a Maduro dictatorship.
Colombia's finance minister earlier Firday told a local radio station that his nation would sanction the same 13 current and former high-level Venezuelan officials cited by the USA government earlier in the week.
The killings took place before voting started to elect a new assembly with powers to rewrite the constitution.
The US, the European Union, the Organization of American States, as well as Argentina, Brazil, Colombia and Mexico oppose the election, warning it could decapitate Venezuela's democracy and lead to further unrest. The opposition leader was recently free from prison and transferred to house arrest.
President Nicolas Maduro was among the first to cast a vote in the so-called constituent assembly, ignoring worldwide condemnation, a boycott by the opposition, and the threat of severe sanctions by the U.S. Maduro, 54, has been derided for the plan to bypass congress as a means for an indefinite power grab.
Venezuelan President Nicolas Maduro is paying homage to the late Hugo Chavez on what would have been his predecessor's 63rd birthday. Even so, the election is wildly unpopular among most Venezuelans; surveys earlier this month showed that almost 8 in 10 opposed rewriting the nation's two-decade-old charter.
The country's prosecutors' office said the circumstances were still to be investigated but an opposition parliamentarian, Henry Ramos Allup, said Mr Campos was shot dead.
In opposition-dominated eastern Caracas, riot police used tear gas to stop protesters from gathering for a march on the capital's main highway.
Interior Minister Nestor Reverol announced Thursday that officials were prohibiting any protests through Tuesday.
He also urged the population to vote with faith, hope and love, stating that the ANC will be the way to rediscover the national spirit, justice and reconciliation among Venezuelans.
Lawmaker Jose Manuel Olivares asked Venezuelans "not to be victims of fear".
Maduro has described the election as the most important Venezuela has seen, and the Constituent Assembly a "card that will win this game".
The migrants are fleeing triple-digit inflation, food and medical shortages and a homicide rate that is among the world's highest. More than 110 people have been killed in recent clashes.
The new legal status does not provide aid to the thousands who entered illegally.
Maduro contends that the government restructuring is necessary to prevent more bloodshed on the streets and save Venezuela's failing economy.
Today, through a secret, direct and worldwide vote, the Venezuelan population elect 537 parliamentarians and the remaining eight members of the assembly will be voted on August 1st amid the indigenous communities of Venezuela.
In a protest in the northeast town of Cumana, a 30-year-old regional secretary for a youth opposition party was shot dead in an anti-election protest.