Candidates aligned with Maduro have won 20 of the 23 governor posts and the mayorship of the capital Caracas in the face of a divided opposition running in an election for the first time in 3 years.
Protesters said they were heeding the opposition's call for another mass demonstration despite the heavy-handed response by security forces over the last week to quell anti-government protests.
Opposition critics slammed the plan as inadequate in the face of inflation that topped 82,000 percent in July and called for a one-day halt of commercial activities.
To date, 14 people have been arrested and charged for allegedly taking part in the August 4 incident in which Maduro was seen reacting on live television to an off-camera explosion .
Maduro, who has systematically sidelined the opposition as he tightens his grip over his troubled nation, accuses the opposition and Colombia of being behind Saturday's drone "attack."
A live broadcast of the incident on Venezuelan state television showed Maduro interrupted in mid-speech by an explosion and looking up in confusion.
Last year, the European Union hit the Venezuelan vice-president and 10 other officials with sanctions over rights abuses and irregularities in the re-election of Maduro.
Venezuela arrests six terrorists over attack on President Nicolas Maduro as opposition fears reprisals
Venezuela's socialist government alleged Sunday that the detained suspects conspired with others in Miami and the capital of neighbouring Colombia, though they offered no specific evidence.
Maduro said he had escaped an "assassination" attempt using an explosive-laden drone during a Caracas military parade, which the government said injured seven soldiers.
Maduro accused neighboring Colombia and unidentified "financiers" in the United States of being behind the blast, while some of his officials blamed Venezuela's opposition.
The head of the assembly, Diosdado Cabello, tweeted that Maduro and the assembled military chiefs had survived a "terrorist attack" he blamed on the opposition.
The UN human rights chief warned on Wednesday that democracy in crisis-torn Venezuela was eroding fast, questioning whether it was still functioning at all.
Venezuela's all-powerful new constituent assembly said Tuesday it will hold treason trials for opposition leaders it said are promoting economic sanctions imposed by the United States.
A new assembly packed with allies of unpopular President Nicolas Maduro and with sweeping powers was to begin work on Saturday, deepening divisions in a crisis-wracked Venezuela.
The US on Monday branded the Venezuelan President a "dictator" threatening his country's democracy and imposed sanctions targeting any assets he might hold on US territory.