Those who signed an initial petition calling for a recall referendum must submit their fingerprints to the electoral authorities in order to authenticate their signatures.
Crowds of citizens holding their identity cards queued up first thing Monday morning to have their prints taken at the National Electoral Council in Caracas. Other collection points were set up around the country.
Of the 1.3 million signatures recorded by the electoral board in the initial petition, at least 200,000 must be authenticated to pass to the next phase.
The next step will require yet more signatures to be collected.
Venezuela is suffering an economic crisis worsened by the plunge in prices for its crucial oil exports.
Citizens are suffering shortages of basic foods and goods.
The opposition says Maduro's economic management is also to blame, and denounce the jailing of his political opponents.
Maduro is resisting efforts for a referendum. He has alleged irregularities in the signature process.
His government said the signatures collected included those of prisoners ineligible to vote.
The country's food crisis erupted into deadly looting last week. Authorities said at least five people were killed and more than 400 arrested.
The president has warned he may decree emergency measures if confronted with violence.
Such measures could prevent the recall referendum from taking place.