Correspondents say opponents of Mr Chavez who want a referendum on his rule are now targeting the oil business as they say they will take a national strike into a fifth day on Friday.
Refinery workers have walked out and the crews of some tankers have refused to dock and deliver their cargoes, forcing oil company officials to tell customers they may not be able to fulfil contracts.
Deputy Oil Minister Bernardo Alvarez warned that the stoppage could generate "irreparable damage" to the stability of Venezuela, which depends on oil exports for most of its revenues.
Mr Chavez marked a new, tougher line on Thursday - the fourth consecutive day of mass demonstrations led by labour unions and business federations - by sending in troops.
In a televised address, he said the strikers were threatening "the heart of the country" by targeting the oil sector.
Naval boats surrounded the Pilin Leon tanker and its cargo of 280,000 barrels of oil after its crew dropped anchor in Lake Maracaibo and joined the strike in what Mr Chavez called "an act of piracy".
Other tankers have also halted their journeys, but it is unclear if the navy will attempt to force them into port or simply monitor the situation, correspondents say.
'Unacceptable' disruption
National Guard soldiers were also sent to guard oil installations at ports paralysed by the stoppages.
Mr Chavez said he could not accept damage to the oil industry.
"It's as if the doctor who's supposed to be looking after your heart suddenly starts trying to stop it," he said in his TV address.
The disruption in Venezuela - the world's fifth largest oil exporter - sent crude prices rising in London and New York.
On Wednesday, the government said it could guarantee exports to its clients but on Thursday Jorge Kamkoff, a vice-president of the state oil company acknowledged that orders could not be filled.
Tipping the balance
In the past few days both opponents and supporters have held mass rallies, many of which have taken place outside the headquarters of the state-owned oil company PDVSA.
Reports say that, so far, the protest movement has been only partially successful.
But the BBC's Steven Cviic says there are two institutions which could tip the balance either way: the army and the state oil firm - both of which are now getting involved.
In April, a similar strike sparked street clashes between pro- and anti-Chavez demonstrators in which at least 19 people were killed.
The protests led to a short-lived coup in which President Chavez was ousted for about 48 hours by rebel military officers, before being reinstated by forces loyal to him.
The Organization of American States is trying to broker talks between the two sides, but the government has refused to negotiate while the strike continues.
Have you been affected by the Venezuelan strikes? Send us your comments.
I'm a high school student and I haven't had classes since Monday, the day the strike began. It's been 4 days and the strike is still on. Despite this, nothing is more valuable than democracy and freedom, both being threatened by the authoritarian and communist-sympathazing government of Chavez. I'll keep supporting the strike and I and my family will "stop" for as long as it is necessary to make my rights respected by the government.
Alexander Marzuka
Venezuela
It is terrible to rise your kids under this regime that is taking away our liberties
Mauro Paez-Pumar
Venezuela
What can the world do for Venezuela? Or we do not deserve international help for our human rights? At this moment, the UN's Blue Helmets are welcomed in our country.
Hector Merino
Venezuela
It would be fair to say that every Venezuelan one speaks to is depressed, worried and anxious and Christmas seems to have been put on hold.
Debby Kemball
Venezuela
I've been marching ever since last year, because I want to have the opportunity to live a decent life. Not under a crazed "president" who wants to imitate Fidel Castro!
Alexandra Heyer
Venezuela
I believe in my country, I believe in God in I believe that Venezuela is going to be better when Chavez is gone.
Alejandro Perez
Venezuela
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