Intermittent clashes have been reported over the last four days between protesters hurling bottles and stones, and police firing rubber bullets and tear gas.
Government supporters also marched in Caracas on Tuesday, celebrating Chavez's decision on Radio Caracas Television (RCTV), state television showed.
Globovision is the last main opposition-linked media in Venezuela to have free-to-air broadcasts but does not have nationwide coverage.
RCTV still offers its programmes via cable and satellite - out of reach of many Venezuelans.
'Enemy of the state'
"I believe that the closing-down of the television station is very justified"
Medishagh, Nouakshott, Mauritania
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Describing Globovision as "enemies of the homeland, particularly those behind the scenes", Chavez told the station to "watch where you are going".
He said on Tuesday in a nationwide broadcast: "I recommend you take a tranquiliser and get into gear, because if not, I am going to do what is necessary."
Chavez also told Venezuelans to be on the alert in case the ongoing protests turned into a coup attempt against him similar to one in 2002.
Many consider a critical local media as the main safeguard against a possibility of sliding into a dictatorship under Chavez, who is forging a single governing party, ruling by decree and considering abolishing limits on the presidential tenure.
Alberto Ravell, Globovision's director-general, denied Chavez's charges but said he was worried by the government's offensive.
He said: "If this government, with one stroke of the pen, closed the oldest television station in the country that has been on the air for 53 years, how will it not be able to shut this station which is far smaller?
"This is a country with a single party and a single trade union. Now it appears there is going to be a single channel."