Maduro, who showed a photo of a white-plaster wall with marks that appear like eyes and a nose, said Chavez's face had briefly appeared to workers building a new subway line in Caracas in the middle of the night.
Speaking on state television, the president said: "My hair stands on end just telling you about it. Who is that face? That gaze is the gaze of the fatherland that is everywhere around us, including in inexplicable phenomena."
Maduro - who was elected president in April after the death of Chavez - has previously spoken of seeing the spirit of his idol several times, including in the shape of a bird.
The US fugitive Edward Snowden has accepted an offer of asylum from Venezuela, according to the AFP news agency.
A lawmaker close to the Kremlin, Duma politician Alexey Pushkov, tweeted that Mr Snowden has accepted an offer of asylum.
A man in a red jacket ran onto the stage during Venezuelan President Nicolas Maduro's inauguration speech today and grabbed the microphone, but was quickly tackled by his bodyguards.
"The security has failed totally. They could have shot me easily," Maduro said after resuming his speech to an audience that included the leaders of Brazil, Iran and Argentina.
Venezuela's electoral authority is to carry out a full audit of electronic votes cast in the country's presidential election.
The announcement, reported by Reuters, comes hours before Nicolas Maduro was due to be sworn in as Hugo Chavez's successor after a narrow victory on Sunday.
The US had already called for a recount of the closely fought poll.
Mr Maduro was declared the winner by the country's National Electoral Council by 262,000 votes from 14.9 million cast by Venezuelans.
The former bus driver rose through the political ranks with his faithful support of the late President.Read the full story ›
Fireworks have been let off in Caracas as Venezuela elected Nicolas Maduro as president - opposition backers banged pots and pans in reaction to the vote result.
Venezuela's ruling party candidate Nicolas Maduro called for peace and said he would be willing for Sunday's election result to be audited after officials said he took 50.76 percent of votes, compared to 49.07 percent for his rival Henrique Capriles.
"We don't want violence, we want peace," Maduro said in a speech to the nation.
"They [the opposition] want an audit, we welcome the audit ... I formally request the National Electoral Commission to carry out an audit."
Venezuela's Nicolas Maduro says he is willing to allow election result audit and calls for peace.
- Read: Venezuela elects Maduro.
Ruling party candidate Nicolas Maduro won Venezuela's presidential election on Sunday with 51 per cent of votes, the electoral authority said, allowing him to carry forward the socialist policies of the late Hugo Chavez.
Maduro's young challenger, Miranda state Governor Henrique Capriles, took 49 percent of the ballots, the authority said, in a tighter-than-expected vote.
Venezuela elects Nicolas Maduro as president in the country's election, the Electoral Authority says.
The election board says the result is irreversible and urges Venezuelans to respect the results and stay indoors.
- Read: Fears over Venezuela vote.
Both sides in an election to choose a successor to Venezuela's late leader Hugo Chavez expressed confidence of victory after Sunday's vote, raising fears that the official result could be contested.
Acting President Nicolas Maduro led all polls before the vote, buoyed by Chavez's blessing before he died from cancer last month and vowing to continue the former president's self-styled socialist revolution.
But Maduro's rival, state governor Henrique Capriles, appeared to close the gap in the last days of the short campaign.
- Read: Fears over Venezuela vote.