President Trump’s escalating demands for investigations into his political opponents have intensified debate over whether his often-transparent calls for action by the Justice Department amount to abusing his power to bolster his re-election prospects.
Mr. Trump called in an interview aired on Sunday for an investigation into business deals in China by Hunter Biden, the son of former Vice President Joseph R. Biden Jr., the Democratic candidate Mr. Trump’s advisers believe could pose the biggest threat to him in 2020.
In recent weeks, Mr. Trump has called for inquiries into the Bidens relating to the younger Mr. Biden’s business in Ukraine, an effort amplified by Rudolph W. Giuliani, the president’s personal lawyer.
“One hundred percent — it’s a disgrace,” Mr. Trump said in an interview with Steve Hilton, a Fox News host, when asked if the Bidens’ supposed financial ties with China should be investigated.
It was the latest in a long series of statements by Mr. Trump suggesting he would like to see criminal investigations of opponents including Hillary Clinton, John Kerry and the Democratic National Committee, and it came as the president seems particularly preoccupied by Mr. Biden’s candidacy.
It also highlighted the pressure on Attorney General William P. Barr to navigate between Mr. Trump’s demands and Mr. Barr’s stated desire — after withering criticism over his handling of the special counsel’s report — to reassert the Justice Department’s independence from politics.
“It’s a terrible breach of norms for the president to publicly advocate prosecutions of his opponents,” said Jack Goldsmith, a professor at Harvard Law School who was an assistant attorney general during President George W. Bush’s first term.
Mr. Goldsmith pointed out that this was not the first time Mr. Trump has intimated he might intervene in the functions of the criminal justice system. But Mr. Goldsmith said that, to date, “his White House and Justice Department subordinates have basically ignored him. Trump has violated norms, but his executive branch officials thus far have not.”
Still, he warned that, even if Mr. Trump’s calls for investigations are not acted upon, they can nonetheless erode confidence in federal law enforcement. “I do worry that the events of the last three years will make every high-profile Justice Department investigation seem crassly political to half the nation,” he said.
Hunter Biden has become a particular target for Mr. Trump and his allies.
They have focused attention on his personal life, including his 2014 discharge from the Navy Reserve after testing positive for cocaine, and his business career, which included a number of roles that intersected with his father’s political career. He worked with a Delaware-based credit card issuer, at the Commerce Department under President Bill Clinton and as a lobbyist on behalf of various universities, associations and companies.
During his father’s second term as vice president, Hunter Biden increased his international business efforts, including with individuals and entities viewed warily by the United States government and its allies.
In addition to his work in Ukraine for the energy company Burisma, Hunter Biden advised a Romanian businessman with ties to the United States, Gabriel Popoviciu, whose real estate dealings had come under investigation, according to people familiar with the arrangement, which has not been previously reported. The investigation, which came as the United States and its allies were pushing Romania to clamp down on corruption, led to Mr. Popoviciu’s conviction and a prison sentence.
In the deal alluded to by Mr. Trump in the Fox News interview on Sunday, Hunter Biden and a business partner, Devon Archer, were involved in a fund that reportedly pursued an investment from the Chinese government-owned Bank of China.
The fund was announced in late 2013 — days after Hunter Biden and one of his daughters flew to China from Japan aboard Air Force Two with the vice president, who was in the midst of a diplomatic mission intended to calm rising tensions in the region. During the trip, Vice President Biden warned Chinese leaders not to use fighter jets to enforce an air defense zone created by Beijing over contested waters.
The conservative author Peter Schweizer has claimed that Hunter Biden used the trip to secure a deal with the Bank of China — a claim that has been echoed by Mr. Trump’s allies in the conservative news media.
But a lawyer for Hunter Biden said he did not conduct any business related to the China investment fund on that trip, and was not an equity owner in the fund while his father was vice president. He later acquired a 10 percent interest in the entity that oversees the fund, but to date has not received any money from the arrangement, according to the lawyer.
Mr. Trump, in the Fox News interview that aired Sunday, mischaracterized the issues surrounding Hunter Biden’s work in Ukraine, claiming that the country’s top prosecutor at the time “was after” Hunter Biden. There is no publicly available evidence that the younger Mr. Biden was a target of any of the cases that were open under the prosecutor, which instead involved the owner of Burisma and his companies.
Mr. Trump also seemed to claim that Vice President Biden told the Ukrainians, “Don’t you dare prosecute” Burisma or its owner. In fact, no evidence has surfaced that the former vice president intentionally tried to help his son by pressing for the prosecutor general’s dismissal.
Hunter Biden and his father never discussed Burisma or the investigations, according to statements from Hunter Biden and his father’s campaign spokeswoman.
And some former Obama administration officials said Vice President Biden never did anything to deter other administration officials who were pushing for the United States to support criminal investigations by Ukrainian and British authorities — and potentially to start its own investigation — into Burisma and its owner.
But the involvement in China and Ukraine concerned a business partner of Mr. Biden and Mr. Archer, Christopher Heinz, the stepson of John Kerry, who was then secretary of state.
Mr. Heinz argued to Mr. Archer, who like Hunter Biden had joined Burisma’s board, that the posts created the appearance of selling influence, according to a person familiar with the conversation. Mr. Archer did not heed the advice. And Mr. Heinz, who was not involved in the China or Ukraine efforts, began decoupling his business interests from those of Mr. Biden and Mr. Archer.
At a news conference this month, Mr. Trump said Mr. Kerry “should be prosecuted” for violating the Logan Act, which prohibits private citizens from interfering in diplomatic relations between foreign governments and the United States. Mr. Trump accused Mr. Kerry of telling the Iranians “not to call” and “telling them what to do.”
A spokesman for Mr. Kerry, Matt Summers, said Mr. Trump was “wrong about the facts” and “wrong about the law.”
Another target of Mr. Trump has been the Democratic National Committee. “These were crimes committed by Crooked Hillary, the DNC, Dirty Cops and others!” he wrote on Twitter. “INVESTIGATE THE INVESTIGATORS!”
On Friday, Mr. Trump accused the F.B.I. of engaging in “treason” and claimed that it had spied on his campaign. He called for a “long” confinement for those responsible, without singling out any individuals.
When Mr. Barr took over as attorney general in February, many Justice Department career employees hoped that he would act as a bulwark against what they saw as the president’s attempts to politicize their work. But Mr. Barr has shown no desire to push back actively against Mr. Trump.
He testified this month before Congress that we “have to stop using the criminal justice process as a political weapon,” but he made those remarks to defend rather than criticize the president.
Mr. Barr said the special counsel’s nearly two-year investigation into the president had been based on false allegations that Mr. Trump had conspired with Russia to sway the election, and he has since reiterated that he will determine whether the origins of the investigation itself were unlawful.
For those who believe that the Justice Department should operate independently from the White House, Mr. Barr’s testimony before the Senate Judiciary Committee this month was worrisome.
When asked by Senator Kamala Harris, Democrat of California, whether anyone at the White House had ever suggested, inferred or asked that the Justice Department investigate anyone, Mr. Barr said he did not understand the question, then said he did not know the answer.
Critics say Mr. Barr has not acted as a neutral arbiter but as a defender of what he sees as expansive presidential power. Mr. Barr has defended himself as appropriately defending the constitutional powers of the presidency.
Given that Mr. Trump does not comply with norms and is willing to push the law as far as he can to get what he wants, “Trump and Barr are a dangerous combination,” said Mark Rozell, a law professor at George Mason University, who wrote a book on executive privilege that examined Mr. Barr’s first stint as attorney general.
“The president doesn’t fundamentally understand the powerfully important role he plays in establishing the nature and operations of our constitutional system,” Mr. Rozell said. “Future administrations will use what he has done to justify all kinds of behaviors and actions that were once unthinkable.”
An earlier version of this article misstated Mark Rozell’s role at George Mason University. He is the dean of the Schar School of Policy and Government, not a law professor.