Prosecutors with special counsel Robert S. Mueller III’s office on Thursday defended their investigation into former Trump campaign chairman Paul Manafort by saying his long-standing ties to Russian-backed politicians, financiers and others warranted a probe into whether any served as “back channels to Russia.”

Deputy Solicitor General Michael R. Dreeben said the focus on Manafort fell well within Mueller’s authorization to investigate Russian interference in the 2016 U.S. election, including “any links” or coordination between Trump campaign associates and the Russian government.

Dreeben’s reference to back channels came during a hearing in federal court in Washington in which Manafort’s attorneys sought to have criminal charges against him dismissed.

Dreeben cited Manafort’s alleged long-standing connections in Russia during a decade of work as an international political consultant in Ukraine and said it was “only natural” to investigate whether those ties were a means of “surreptitious communications. Did they provide back channels to Russia?”

Prosecutors’ sharpened rhetoric came as Manafort’s attorneys argued that Mueller exceeded his authority by charging Manafort with numerous felonies, including conspiracy, bank and tax fraud, and money laundering, related to work before 2014 on behalf of Ukraine’s pro-Russian president at the time, Viktor Yanukovych.

Manafort joined the Trump campaign in March 2016 and resigned that August amid news reports about his activities in Ukraine.

Manafort’s attorneys contend Deputy Attorney General Rod J. Rosenstein acted improperly when he appointed Mueller in May 2017 to investigate not only any campaign collusion with Russia but any other issues that “may arise” from that investigation.

His attorneys asserted that Manafort is charged for conduct that predated the campaign, and that the authorization for Mueller’s probe is so broad it violated department regulations that they said require a “specific factual statement” of matters under investigation.

Manafort, 69, has pleaded not guilty to all counts in the indictment in the District and also to federal charges in an indictment in Virginia for alleged bank fraud and false tax filings.

U.S. District Judge Amy Berman Jackson appeared skeptical of the motion to dismiss the charges in the District, noting that Manafort was a senior Trump campaign official and someone with Russia ties.

“Mr. Manafort falls on both sides of that line,” Jackson said. “And don’t you have a conspiracy count in the indictment that includes that conduct that goes into 2016?” Jackson asked.

“We do,” defense attorney Kevin M. Downing acknowledged.

Still, Downing said that Rosenstein gave Mueller a “blank check” in what to pursue in the probe. In effect, “Mr. Rosenstein said to Mr. Mueller, ‘Go do it. You’ve got it, do what you want,’ ” Downing argued.

Congress let a statute on court-appointed independent counsels expire in 1999 largely because of concerns about runaway prosecutions, Manafort’s attorneys suggested, but said that if it has been replaced by a system in which “an attorney general can do whatever he wants” by appointing a special counsel with open-ended jurisdiction without any court review, “We are in a worse place than when we were” before.

Thursday’s hearing marked a sharper clash on the same set of issues raised in a lawsuit by Manafort that was argued April 4 before Jackson. The judge then appeared dismissive of Mana­fort’s bid to block Mueller from filing future criminal charges against him.

The same questions will be tested again on May 7 in Virginia, where Manafort has moved to toss out a second criminal case brought by the special counsel.

On Thursday, Manafort’s attorneys urged the judge to order the Justice Department to turn over more documents about the timing and scope of Mueller’s investigation.

Downing focused his fire on a recent disclosure by prosecutors that Rosenstein issued a second “scope” memo on Aug. 2, 2017, that specifically authorized Mueller to investigate Manafort’s Ukraine work and whether he “committed a crime or crimes by colluding with Russian government officials.”

“It seems to me very much an after-the-fact justification for something that on August 2, Mr. Rosenstein maybe recognized he got wrong on May 17,” Downing said, asking for more transparency and a paper trail from Rosenstein. “I don’t know what happened, but if you could have the record, we would all know the reasons, and we could resolve this right now.”

In her questions, Jackson suggested Downing was “cherry-picking” two unrelated sentences of a Justice Department regulation meant to spell out how the department decides internally which prosecutors will handle which cases — not, as Downing argued, to let defendants challenge who is to be investigated

Dreeben said it would be extraordinary overreach “to pull back the curtain” of internal “personnel” and prosecutorial decision-making by an “alive and awake” deputy attorney general actively supervising a special counsel who is “not on a frolic and on a detour” from investigating what he was charged to do.

Jackson picked up that line, asking Downing at one point, “You want me to assume that in one of the most high-profile and complicated investigations . . . a career department official [Rosenstein] appointed the former director of the FBI and a former U.S. attorney [Mueller], you’re telling me he didn’t tell him what he was to investigate?”

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