Henrique Capriles said 37% of the 195,000 signatures needed to trigger the next phase of the recall referendum were collected on the first day.
Those who endorsed the petition have until Friday to have their identity checked.
Mr Maduro's term runs until 2019.
But the opposition wants to oust President Maduro, whom they blame for Venezuela's economic problems, before the end of his term.
Venezuela is in the midst of an economic crisis which has brought the South American country to the brink of collapse.
What has gone wrong in Venezuela?
Chavez backer decries anarchy
It has the world's highest inflation rate and chronic shortages of basic food and medicine.
Mr Capriles said the massive presence of voters on the first day of the validation process was a clear sign that Venezuelans wanted a change of government.
"What we saw today were queues across the country," said Mr Capriles on Monday night. "That's a warning for Maduro."
Those who endorsed the petition will have until Friday to have their identity cards and fingerprints checked at centres set up by the National Electoral Council (CNE).
The petition had almost two million signatures but election officials said 600,000 of those were fraudulent.
Only 1% of the electorate, or 194,729 voters, however, need to endorse the referendum in this first phase.
Mr Capriles said 71,557 signatures had been authenticated on Monday alone.
But the opposition still has to overcome a number of hurdles before a recall referendum can be held.
If enough signatures on this initial petition are validated, opposition leaders will have to hand in a second petition signed by almost four million people.
Only when the electoral authorities have established that the requirements have been met on that second petition will the recall referendum be held.
The process of validating signatures on a petition calling for a referendum to remove Venezuelan President Nicolas Maduro from office is proceeding apace, an opposition leader says.