Maduro had rallied his supporters to turn out for a counter march Wednesday, and thousands showed up wearing the red clothing that marked them as Chavistas.
Click through the gallery to see the clashes.
The 28-nation bloc also called for an investigation to identify those responsible for the violence, as opponents vowed to hold fresh rallies to oust President Nicolas Maduro.
Anti-government protesters have described it as Venezuela's "second independence day".
Further fueling the protests: The government banned opposition leader Henrique Capriles from all political activity for 15 years on April 7.
A government U-turn on the move failed to quell the violent opposition protests that swiftly followed. Tens of thousands of opponents of President Nicolas Maduro flooded the streets of auto.
The Maduro government's seizure of US -based General Motors' sole factory in Venezuela is likely to add to Tillerson's worries.
The State Department and several regional governments have deplored excessive violence by security forces and pro-government groups.
The seizure arose from an nearly 20-year-old lawsuit brought by a former GM dealership in western Venezuela. "If we were millions today, tomorrow we'll be more".
Later that day, the government also seized General Motors' plant in Venezuela.
Venezuela has seen demonstrators take to the streets in protest against President Nicolas Maduro.
Tillerson said the United States was working with the Organization of American States to express these concerns to Venezuela.
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"This is a test case for Trump", said Raul Gallegos, a Bogota-based analyst at Control Risks consultancy.
U.S. Sen. Marco Rubio is criticizing the Venezuelan government over the seizure of General Motors assembly plant in the South American nation.
A message from the president broadcast on television and radio stations Thursday said: "I denounce Movistar de Venezuela and have asked for an investigation because they have joined the calls for a coup in the country and that is not their function". In June, a state of emergency was called, with Maduro blaming the USA and neighboring Colombia for having caused the crisis.
Maduro didn't provide evidence to back his claim that a coup attempt was under way, and the opposition rejected his comments as a desperate attempt to intimidate Venezuelans from exercising their constitutional right to protest. At least two dead during mass protests.
Thousands of Venezuelans have gathered in the capital in anti-government protests, calling for a new presidential election.
Across the country, the clashes have been intense.
"Everyone is out of danger", Muchaco said on his Twitter account. "That's how this criminal dictatorship works".
A national guardsman was killed south of the capital. Another officer was wounded in the clashes.
The march followed a fortnight of violent protests triggered by a Supreme Court decision in March to assume the powers of the opposition-led Congress - which it quickly reversed under global pressure.
The Supreme Court's decision has energized Venezuela's fractious opposition, which had been struggling to channel growing disgust with Maduro over widespread food shortages, triple-digit inflation and rampant crime.
The elections council, which is sympathetic to the government, has delayed votes for state governors which were supposed to take place previous year.
In recent days, Maduro ordered troops to fan out around the country on high alert, and he encouraged his backers, including civilian militia members, to defend against alleged plans to overthrow his government.
Ricardo Rios, a mathematics professor at Central University in Caracas, said that Wednesday's march, organized by a coalition of opposition parties, was larger than the last major demonstration in September.