The special counsel’s loss of two possible cooperating witnesses who could describe the inner workings of the Trump campaign and possible ties to the publisher of hacked Democratic emails is a setback to the investigation, but not a fatal one, legal analysts said.

Former Trump campaign chairman Paul Manafort probably will never take the stand as Robert S. Mueller III’s star witness. And Mueller’s prosecutors might have to plow deeper into the world of WikiLeaks and its contacts to determine what, if any, coordination occurred between the Trump campaign and Russia over the release of emails.

That probably will leave Mueller disappointed but undeterred — perhaps now more mindful of the pitfalls of exploring a world that has an estranged relationship with the truth, legal analysts say.

“I certainly don’t see this as a critical problem,” said David S. Kris, a former Justice Department national security official and the founder of Culper Partners. “It’s just a development that has to be dealt with.”

Mueller has so far charged 32 people in connection with the probe, extracting guilty pleas from several, delving deeply into Russian influence and hacking operations, and compiling reams of unrevealed evidence through a grand jury. What remains to be seen is whether Mueller will make public findings that definitively link the Trump campaign and Russia in 2016 election interference, and to what extent, if any, he might accuse the president himself of wrongdoing.

Mueller’s team alleged in a Monday night court filing that Manafort, who after months of resistance had agreed to cooperate fully with the investigation, was still lying to them. The revelation came just as conservative author Jerome Corsi, whom Mueller has investigated as part of his examination of possible ties between WikiLeaks and the Trump campaign, said publicly he was rejecting a plea offer from the special counsel.

In the run-up to the midterm elections, Mueller’s team had effectively gone dark — following Justice Department policies that discourage prosecutors from taking overt steps in election-related cases close to the time ballots are cast. With the election over, observers had expected that the special counsel might break his silence with indictments that speak to possible coordination between the Kremlin and the Trump campaign.

That has not happened. And Mueller’s political footing seems to have become more unsteady.

President Trump installed Matthew G. Whitaker — a former U.S. attorney and legal commentator who had been publicly skeptical of the special counsel probe — to serve as acting attorney general after firing Jeff Sessions. Whitaker nominally took over supervising Mueller from Deputy Attorney General Rod J. Rosenstein, who had been in charge because Sessions recused himself.

Whitaker so far has kept a low profile — not taking any steps that have become public to interfere with the Mueller probe. Democrats and others fear he might block Mueller from making aggressive moves, such as forcing Trump to testify with a subpoena.

A spokesman for the special counsel’s office did not return a message seeking comment.

On Tuesday, Trump launched a fresh round of attacks against Mueller, suggesting that he was closely following Manafort’s and Corsi’s evolving legal situations.

“The Phony Witch Hunt continues, but Mueller and his gang of Angry Dems are only looking at one side, not the other. Wait until it comes out how horribly & viciously they are treating people, ruining lives for them refusing to lie. Mueller is a conflicted prosecutor gone rogue,” he wrote on Twitter.

Corsi, an associate of Roger Stone, a longtime private Trump adviser, had alleged that the plea deal Mueller offered would have required him to say that he intentionally deceived investigators, when he contended he was simply forgetful in responding to questions about his interest in WikiLeaks’ activities.

A statement of offense that Corsi provided to The Washington Post on Tuesday alleges that Corsi told Stone in early August 2016 that WikiLeaks planned two more releases of emails that could be damaging to Hillary Clinton’s campaign and mentioned campaign chairman John Podesta. WikiLeaks released a batch of Podesta’s emails — which authorities have alleged were stolen by Russia — in October of that year.

The statement, a court document that would have described the wrongdoing to which Corsi was admitting, alleges that Corsi lied to investigators about his WikiLeaks-related dealings with Stone — falsely saying he declined a request from Stone to get in touch with WikiLeaks in the summer of 2016 when in fact he had passed on the request to another person in London. Julian Assange, the founder of WikiLeaks, is living in the Ecuadoran Embassy in London, having been granted asylum there by the South American country.

Corsi told The Washington Post on Tuesday that he had exaggerated his knowledge of WikiLeaks’ plans. Stone and WikiLeaks have denied any coordination on the email release.

Even before their sudden recalcitrance, both Corsi and Manafort would probably have made less than ideal witnesses for Mueller’s investigation because of questions about their credibility.

Corsi is a known conspiracy theorist who falsely asserts, among other things, that President Obama was not born in the United States. Before he agreed to plead guilty, Manafort had been convicted of tax and bank fraud.

Analysts say the pair are emblematic of a challenge Mueller has long faced. Several of his cooperators — former national security adviser Michael Flynn, former deputy campaign chairman Rick Gates and former campaign adviser George Papadopoulos — are admitted liars.

That is not uncommon: The best witnesses to crimes are often criminals themselves. But white-collar defendants can pose unique challenges, analysts said.

“Give me a shameless sociopath over a dissembling fraudster any day,” said James M. Trusty, a former chief of the Justice Department’s Organized Crime Section now in private practice at Ifrah Law. “We would have gang members who would just sit down and without a blink of an eye tell us about murders we had no idea about . . . The other side of the spectrum is you get these well-heeled white-collar defendants who have been rationalizing for a long time. Everything becomes a ‘what is is,’ where you have to play chess with them every second to get the truth out.

Legal analysts noted that Mueller poured immense resources into winning Manafort’s cooperation, probably hoping he might share critical information. The special counsel’s office put Manafort through a weeks-long trial on tax and bank fraud charges, and then — after winning a conviction — persuaded him to plead guilty in a separate case in the District.

Special counsel investigators had met with him several times after that, although it is unclear what Manafort told them. In the Monday court filing, the special counsel’s office said Manafort had lied “on a variety of subject matters, which constitute breaches of the agreement.”

Manafort’s legal team said in the same filing that Manafort “believes he has provided truthful information and does not agree with the government’s characterization or that he has breached the agreement.”

“The whole thing is a debacle,” Trusty said. “Not that Manafort shouldn’t have been prosecuted in the abstract, but it is a rabbit hole, and the rabbit hole has gotten considerably deeper and wider with this recent turn of events.”

Former U.S. attorney Barbara McQuade said she questions why Manafort would lie, as it essentially eliminates all the benefit he would get from his plea deal with prosecutors.

“There’s no self-interested reason to lie at that point,” McQuade said. “The only reason you might lie is if you want to protect someone else. So you have to ask yourself, ‘who might Manafort be trying to protect?’ ”

Analysts said Mueller’s next move probably will be to throw the book at Manafort — airing evidence of his lies and sending a message to other possible witnesses that those who do not cooperate will face severe punishment.

Prosecutors said they would also “file a detailed sentencing submission” that describes “the nature of the defendant’s crimes and lies, including those after signing the plea agreement herein.”

Corsi’s situation is perhaps more fluid. Like Corsi, former Trump campaign adviser Sam Nunberg had threatened to take a scorched-earth approach with Mueller by ignoring a grand jury subpoena, but less than 24 hours later, he took it all back.Corsi himself had said earlier this month his cooperation with Mueller had “exploded” and he expected to be indicted, but talks seemed to resume after that.

If Corsi holds fast, analysts said, Mueller is likely to charge him. Then comes the hard part: sorting through the lies to prove him or others guilty in court.

“The key is do you have experienced prosecutors and agents that are sifting through the garbage and corroborating the good stuff to the satisfaction of investigators, and also the potential satisfaction of a jury someday,” Trusty said.

Rosalind S. Helderman, Carol D. Leonnig and Manuel Roig-Franzia contributed to this report.