WASHINGTON — The former deputy attorney general Rod J. Rosenstein defended during congressional testimony on Wednesday his decision to appoint a special counsel for the Trump-Russia investigation, as Republican allies of President Donald Trump sought to keep a skeptical spotlight on the inquiry heading into the November election.

“I still believe it was the right decision under the circumstances,” Rosenstein said to the Senate Judiciary Committee about appointing Robert Mueller as special counsel. “I recognize that people can criticize me for them. That’s the consequence of being in these jobs — you make decisions and people criticize you for them — but I believed it was the right decision at the time.”

But Rosenstein also said he would not have signed an application in June 2017 to renew a court wiretap order targeting Carter Page, a former Trump campaign adviser, if he had known at the time that it contained factual errors and omissions, as an inspector general found.

The Republican chairman of the Judiciary Committee, Sen. Lindsey Graham of South Carolina, has made clear that he intends to try to keep a focus in the coming months on the investigators who sought to understand the scope of Russia’s election interference and ties to Trump campaign associates.

Graham and Sen. Ron Johnson, R-Wis., who is chairman of the Homeland Security and Governmental Affairs Committee, plan to ask their panels on Thursday to empower them to issue subpoenas related to the Russia investigation. Those would seek reams of records and testimony from dozens of current and former law enforcement and national security officials, including prominent members of the Obama administration.

The session was the first major investigative hearing the Senate has had in months, scheduled despite the economic and health crises caused by the coronavirus pandemic and amid days of national unrest over police brutality. Democrats insisted repeatedly on Wednesday that those were far more obvious and urgent topics for the Senate’s consideration than an investigation that has already been widely scrutinized.

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“I just do not understand why we as a committee are focusing on things that further deepen the discords of partisan posturing in America,” said Sen. Cory Booker, D-N.J. and one of only three black senators. “I might be missing something, but to me we are in a pandemic like we have not seen since 1918, an economic crisis like we have not seen since the Depression and uprisings across America like we have not seen since 1968.”

Rosenstein was sworn in to the No. 2 post at the Justice Department just weeks before the president fired James B. Comey as the FBI director, and within days Trump publicly and privately linked the dismissal to the Russia investigation. Rosenstein then called Mueller, a former FBI director and prosecutor, out of retirement to lead the inquiry.

Mueller’s investigators found that while the Russian government covertly intervened in the 2016 election with a goal of helping Trump defeat Hillary Clinton, and while the Trump campaign welcomed that assistance and had many links to Russian figures, the evidence was insufficient to prove any criminal conspiracy.

Republican and Democratic senators used the questioning of Rosenstein as a proxy to argue about whether the investigation was justified, given Mueller’s findings. Rosenstein defended the investigation while casting Trump’s long-standing attacks as understandable grievances.

“I do not consider the investigation to be corrupt, Senator, but I certainly understand the president’s frustration given the outcome,” Rosenstein said to Sen. Richard J. Durbin, D-Ill.

Lawmakers also jostled over the findings in December by the Justice Department’s independent inspector general, Michael E. Horowitz. He concluded that the Russia investigation had a lawful basis and found no evidence of political bias in its opening, but uncovered serious errors and omissions by the FBI in applications to obtain a wiretap order under the Foreign Intelligence Surveillance Act, or FISA, targeting Page in October 2016, as well as three renewal orders in 2017.

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The Justice Department has since told a court that it did not think the available evidence met the legal standard to keep invading Page’s privacy for the last two renewals. While Rosenstein was not involved in the early iterations of monitoring Page, he signed off on the third and final renewal application for surveillance.

Rosenstein blamed the FBI for the problems, citing the inspector general’s findings that the bureau failed to follow its procedures and that blamed management breakdowns.

But Republicans found Rosenstein’s explanations unpersuasive and, as the hearing went on, began to criticize him for obfuscating and failing to correct what they argued were blatant abuses of the system he oversaw.

“You came into a profoundly politicized world, yet all of this was allowed to go forward under your leadership,” said Sen. Ted Cruz, R-Texas. “That unfortunately leads to only two possible conclusions: either that you were complicit in the wrongdoing, which I don’t believe was the case, or that your performance of your duties was grossly negligent.”

But Democrats accused Republicans of misrepresenting the investigation for political gain. The hearing in particular highlighted a partisan split over the significance of the flaws in a dossier compiled by Christopher Steele, a former British intelligence agent whose research was funded by Democrats, that included allegations about Page.

Republicans repeatedly sought to keep the focus on the dossier, sometimes overtly conflating it with the larger Russia investigation. For example, Sen. Josh Hawley, R-Mo., accused Democrats on the committee of contending that the Mueller report was of “no consequence” and then pivoted to the use of the dossier in the wiretap applications as if they and the report were the same thing.

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“Now we hear from person after person on that side of the dais that the Mueller report is of no consequence. No consequence?” he thundered, before seamlessly shifting into denouncing the use of the Steele dossier information in the wiretap applications.

None of the Democratic senators had said the Mueller report was of no consequence. But they did repeatedly seek to distinguish the larger Russia investigation and the eventual Mueller report from the use of Steele dossier information in the wiretap applications. They asked Rosenstein questions that focused on the facts that none of Mueller’s findings, nor any of the criminal charges brought by his office, relied upon information from the Steele dossier — and that Page’s name appears on only a handful of pages of the lengthy report.

Sen. Dianne Feinstein, D-Calif., noted that the FBI officials who opened the inquiry “had not even seen the Steele dossier, but because the Steele dossier was cited in the Carter Page FISA applications, the president and his allies falsely claim that the entire Russia investigation” would never have happened but for the document.

Rosenstein also denied making provocative suggestions in the chaotic days after Comey’s firing to both secretly record his conversations with the president as part of any investigation into whether the dismissal constituted obstruction of justice and to recruit Cabinet members to invoke the 25th Amendment to remove Trump.

“I did not suggest or hint at secretly recording President Trump,” Rosenstein said in response to questions from Sen. Mazie K. Hirono, D-Hawaii. “I have never in any way suggested that the president be removed from office under the 25th Amendment. I can give you a more detailed explanation if you have time.”

Andrew G. McCabe, who served as acting FBI director after Comey’s firing, has described Rosenstein’s comments in television interviews and documented them at the time in a memo that has since become public. Another former law enforcement official relayed McCabe’s account to congressional investigators.

When The New York Times first reported on Rosenstein’s comments in 2018, a Justice Department spokeswoman provided a statement from an official present for one of the times when Rosenstein suggested wearing a wire who acknowledged that he had made the remark. The official, however, said Rosenstein was being sarcastic.