"Some say Chavez is backtracking. Well, whoever wants to see it that way can see it that way. No, I move on."
Critics said the law would have obliged citizens to spy on each other, and Chavez has since said that the law had "errors" and must be "corrected" by congress.
Demonstrators have held up signs depicting toads – the Venezuelan term for people who inform on their neighbours.
Human rights groups and the Roman Catholic Church also criticised the decree.
The latest move by the president follows another change of position on Sunday when he urged Colombia's Farc rebels to lay down their weapons and unilaterally release their hostages.
Five-months ago Chavez had urged world leaders to back the left-wing group's armed struggle.
First elected in 1998, Chavez is still trying to recover from the defeat in December of a constitutional referendum that would have enabled him to run for re-election indefinitely and extend his power in other ways.
His party is facing elections in November and Chavez is seeking support for another referendum in 2010 to end term limits on his presidency.
"Chavez cannot be oblivious to the public reaction" as the elections near, said Teodoro Petkoff, a political opponent who now edits the daily newspaper Tal Cual.
"He doesn't want too many polemical issues circling around."