Venezuela’s new leader is a socialist true believer who helped Nicolás Maduro maintain his grip on power for more than a decade as the country’s economy crumbled.

Now, President Trump is counting on leftist Delcy Rodríguez—Maduro’s vice president who became the country’s de facto leader on Saturday—to work with the U.S. as it, in Trump’s words, begins to run Venezuela.

In doing so, he is leaving Maduro’s regime intact and choosing one of the deposed leader’s confidants over Maria Corina Machado , the Nobel Peace Prize-winning opposition leader and right-wing supporter of Trump.

At his news conference Saturday, Trump said that Rodríguez had a long conversation with Secretary of State Marco Rubio . Trump said that as Venezuela’s new de facto leader, she agreed to do whatever the U.S. needed done.

“She, I think, was quite gracious, but she really doesn’t have a choice,” Trump said. “She is essentially willing to do what we think is necessary to make Venezuela great again. Very simple.”

Hours after Trump’s news conference, Rodríguez took a radically different tone, slamming the U.S. for its attack on Venezuelan military facilities as special forces soldiers snatched Maduro and swept him off to the U.S. She demanded the U.S. return Maduro, calling him Venezuela’s rightful president.

“Never again will we be slaves, never again will we be a colony of any empire,” she said, flanked by senior officials from Maduro’s government. “We’re ready to defend Venezuela.”

The fate of the Maduro regime’s remnants now lies in which path Rodríguez takes—the way of defiance against Trump, or working with his administration to stay in power.

Rodríguez, a 56-year-old lawyer by training, has been described by former colleagues and U.S. officials as a ruthlessly ambitious and Machiavellian political operative. For the last decade, she has held a number of key positions as she climbed her way to the top of Maduro’s authoritarian regime.

Venezuela’s President Nicolas Maduro, center, with his wife Cilia Flores, left, and Constitutional Assembly President Delcy Rodriguez wave as they arrive to the National Assembly building for a session with the Constitutional Assembly in Caracas, Venezuela, Thursday, Aug. 10, 2017. (AP Photo/Ariana Cubillos)

She worked hand-in-glove with her brother, Jorge Rodríguez , a trained psychiatrist who now presides over Venezuela’s Congress. Both are considered to be among Maduro’s most loyal lieutenants.

“They are very, very manipulative,” said Andrés Izarra , a former minister under Maduro who now lives in exile after breaking with the regime. “I think they will maneuver to stay in power as long as they can.”

It is bad news for Venezuela’s opposition leader , Machado, who has been a strong supporter of the Trump administration’s campaign against Maduro. Machado had hoped that Maduro’s downfall would usher the opposition into power. But on Saturday, Trump said that while Machado is a “very nice woman,” she doesn’t have the support or respect inside Venezuela to govern.

“None of this looks good for Maria Corina Machado,” said David Smilde, a Venezuela scholar at Tulane University. “In the short term, it doesn’t look like Maria Corina will have much of a role.”

Rodríguez held senior positions in the government of Hugo Chávez , the late socialist firebrand and Maduro’s mentor who took power in 1999. Chávez, a former tank commander who once staged a failed military coup, was elected amid a backlash against an entrenched Venezuelan elite that oversaw the country growing rich with oil wealth but was also regarded as corrupt.

Under Maduro, the Rodríguez siblings became pillars of his regime, with Jorge playing a vital role overseeing a fraudulent election last year that allowed Maduro to remain in power.

Delcy ran the foreign ministry and later took charge of the economy and its most important industry, oil. She was brought in to turn around one of the world’s biggest economic implosions in modern history. More than eight million Venezuelans emigrated as the economy contracted by 80% since Maduro took office in 2013.

“We’ll make the people of Venezuela rich,” Trump said as he announced plans to take over the oil industry in the country with the largest oil reserves in the world.

Rodríguez is known to have a taste for luxury items, favoring designer bags and shoes—a trait opponents have seized on to show her as out of touch with Venezuelans who suffered under Maduro’s rule.

Across much of the country on Saturday, long lines formed at supermarkets and gas stations amid a tense calm, occasionally interrupted by the presence of militant leftist groups aligned with the regime known as Colectivos.

Rodríguez maintains a close relationship with the Cuban intelligence operatives that Maduro has long relied on to root out traitors in his ranks, according to opposition members. Havana views her as a reliable ideological ally and a guardian of Cuban strategic interests within the regime, these people said.

Her father, Jorge Antonio Rodríguez , was a Marxist guerrilla and co-founder of the Socialist League, a militant leftist movement active in the 1960s and 1970s. Rodríguez blames her asthma on a visit she made as a child to her father in prison. She was pushed into the cell where her father was being held and then the secret police set off a tear gas grenade, said Brian Naranjo, a former senior U.S. diplomat who served in Venezuela.

“All her hate for Venezuela’s old political establishment goes back to that abuse,” he said.

In 1976, her father orchestrated the kidnapping of William F. Niehous , a U.S. executive at Owens-Illinois, a manufacturer of glass containers. Accused by his kidnappers of having links to the Central Intelligence Agency, Niehous was held for more than three years before his release in June 1979.

Shortly after directing the abduction, the elder Rodríguez was arrested and died in state custody in 1976 as a result of torture by officers of Venezuela’s secret police.

Rodríguez was seven years old at the time. This legacy of armed struggle, ideological martyrdom, and anti-imperialist narrative shaped her and her brother.

“The revolution is our revenge for the death of our father,” Rodríguez said, according to local media

The idea of Rodríguez taking over power from Maduro had previously been proposed by Qatar as a way to resolve the standoff with the U.S. and Venezuela’s opposition, according to a former senior U.S. official who worked on Venezuelan issues. Until now, Washington hadn’t accepted that idea, the former official said.

To rule the country, she will need to rely on other key, hardline actors in the Maduro regime, particularly Interior Minister Diosdado Cabello , who has been widely accused of human rights abuses. Another crucial apparatchik is Defense Minister Vladimir Padrino . Both men have been indicted in the U.S. on drug smuggling charges. The U.S. has offered a reward of $25 million for information leading to Cabello’s arrest and/or conviction and $15 million for Padrino.

Write to Ryan Dubé at ryan.dube@wsj.com and José de Córdoba at jose.decordoba@wsj.com