Maduro is in a New York detention centre awaiting a Monday court appearance on drug charges after US President Donald Trump ordered his removal.
In the capital Caracas, top officials in Maduro's government, who have called the detentions of Maduro and his wife Cilia Flores a kidnapping, were still in charge.
"Here, the unity of the revolutionary force is more than guaranteed, and here there is only one president, whose name is Nicolas Maduro Moros. Let no one fall for the enemy's provocations," Interior Minister Diosdado Cabello said in an audio shared by the ruling PSUV socialist party on Sunday as he urged calm.
Images of the 63-year-old Maduro blindfolded and handcuffed on Saturday stunned Venezuelans.
The action is the most controversial US intervention in Latin America since the invasion of Panama 37 years ago.
Vice President Delcy Rodriguez - who also serves as oil minister - has taken over as interim leader with the blessing of Venezuela's top court although she has said Maduro remains president.
Because of her connections with the private sector and her deep knowledge of oil, the country's top source of revenue, Rodriguez has long been considered the most pragmatic member of Maduro's inner circle but she has publicly contradicted Trump on his claims she is willing to work with the US.
The Venezuelan armed forces recognises the vice president as the country's interim leader, Defence Minister Vladimir Padrino said on Sunday.
The Venezuelan government has said for months that a US pressure campaign is an effort to take possession of the country's vast natural resources, especially its oil, and officials have made much of Trump's comments on Saturday on the subject, when he said major US oil companies would move in.
"We are outraged because in the end everything was revealed - it was revealed that they only want our oil," said Cabello, who has close ties to the military.
Once one of the most prosperous countries in Latin America, Venezuela's economy nosedived further under Maduro, sending about one in five Venezuelans abroad in one of the world's biggest exoduses.
Maduro opponents in Venezuela have been wary of celebrating his seizure and extraction - and the presence of security forces seemed, if anything, lighter than usual on Sunday.
Despite the nervous mood, some bakeries and coffee shops were open and joggers and cyclists were out like a normal Sunday morning.
Some citizens were stocking up on essentials.
The owner of a small supermarket in the same city said the business did not open on Saturday after US Special Forces swooped in on helicopters to seize Maduro after strikes on military installations in Caracas and elsewhere.
"Today we'll work until noon since we're close to many neighbourhoods - people have nowhere to buy food and we need to help them," the shop owner said.
To the disappointment of Venezuela's opposition, Trump has given short shrift to the idea of 58-year-old opposition leader and Nobel Peace Prize winner Maria Corina Machado taking over, saying she lacked support.
Machado was banned from standing in the 2024 election but has said her ally Edmundo Gonzalez, 76, who the opposition and some international observers say overwhelmingly won that vote, has a democratic mandate to take the presidency.
The United States will "run" Venezuela until a "safe, proper and judicious transition" can be ensured, Trump said on Saturday.
It is unclear just how Trump plans to oversee Venezuela and his focus on foreign affairs runs the risk of alienating some of the US president's domestic supporters who oppose foreign interventions.
The United Nations Security Council planned to meet on Monday to discuss the US attack, which Secretary-General Antonio Guterres described as a dangerous precedent.
Maduro was indicted in 2020 on US charges including narco-terrorism conspiracy.
He has always denied any criminal involvement.
with DPA
