In the biggest US intervention in Latin America since the 1989 invasion of Panama, Special Forces swooped into Caracas on helicopters at the weekend to smash through Maduro's security cordon and nab him at the door of a safe room.
Maduro loyalists remain in charge of Venezuela, first spitting defiance then pivoting to possible co-operation.
Though denouncing Maduro as a dictator and drug kingpin, who flooded the US with cocaine, Trump has made no bones about wanting to share in Venezuela's oil riches.
It has the world's largest reserves - about 303 billion barrels, mostly heavy oil in the Orinoco region. But the sector has long been in decline from mismanagement, under-investment and US sanctions, averaging 1.1 million bpd output last year, a third of its heyday in the 1970s.
After first denouncing Maduro's capture as a colonial oil-grab and "kidnapping", Venezuela's acting president Delcy Rodriguez changed her tune on Sunday, saying it was a priority to have respectful relations with Washington.
"We invite the US government to work together on an agenda of co-operation oriented towards shared development within the framework of international law to strengthen lasting community coexistence," Rodriguez said.
"President Donald Trump, our peoples and our region deserve peace and dialogue, not war."
The daughter of a leftist guerrilla fighter, 56-year-old Rodriguez has been a staunch and fiery-talking member of the ruling "Chavista" movement - named for late leader Hugo Chavez - earning her praise as a "tigress" from Maduro.
But she is also known as a pragmatist with good connections in the private sector and a belief in economic orthodoxy. Many Venezuelans know her for the luxury clothes she likes to wear.
Prior to her statement, Trump had said he could order another strike if Venezuela does not co-operate with US efforts to open up its oil industry and stop drug trafficking.
Trump also threatened action in Colombia and Mexico and said Cuba's communist government "looks like it's ready to fall" on its own.
Just how the US would work with a post-Maduro government, full of sworn ideological enemies, is unclear. He appears to have sidelined for now the Venezuelan opposition, where many anti-Maduro activists had assumed this would be their moment.
Amid global consternation at Trump's seizure of a foreign head of state - albeit an unpopular one - the UN Security Council was due to debate its legality and implications.
Russia, China and leftist allies of Venezuela have condemned the US for violating international law.
Venezuela's staunchest backer Cuba, long rumoured to be in charge of Maduro's security, said 32 of its military and intelligence personnel died during the US raid to extract him.
Washington's allies - most of whom did not recognise Maduro as president due to vote-rigging allegations - have been more muted, stressing the need for dialogue and adherence to law while not openly condemning Trump. Some welcomed Maduro's exit.
The US has a veto to block any Security Council motions.
Maduro, a 63-year-old former bus driver, union leader and foreign minister named by the dying Chavez to replace him in 2013, is in jail in Brooklyn, along with his wife Cilia Flores.
They were due in Manhattan federal court on Monday.
Maduro is accused of overseeing a cocaine-trafficking network that partnered with violent groups including Mexico's Sinaloa and Zetas cartels, Colombian FARC rebels and Venezuela's Tren de Aragua gang.
Maduro has long denied all the allegations, saying they were a mask for imperialist designs on Venezuela's oil.
Trump has also justified Maduro's capture as a response to an influx of Venezuelan immigrants - one in five have left the country in recent years during an economic collapse - and the nationalisation of US oil interests decades ago.
"We're taking back what they stole," he said on Sunday, adding that US oil companies will return to Venezuela and rebuild the creaking industry.
"We're in charge."
Inside Venezuela, Maduro opponents have kept celebrations on hold as his senior loyalists remain in power and there is no sign of the military turning against them, even though many suspect some insiders helped in Saturday's operation.
On the streets, Venezuelans have been stocking up on food and medicines in case of instability, but streets are quieter than normal as everyone wonders what is coming next.
On global markets, Venezuela's default-stricken government bonds surged, oil prices edged up, while stock markets rose in Asia and Europe as investors bought defence stocks after the raid on Venezuela stirred fresh geopolitical concerns.
