A top Justice Department official testified Monday that one-time Obama White House counsel Greg Craig misled her investigators about his work on behalf of Ukraine, convincing them that he didn’t need to register as a foreign agent.

Another witness said Mr. Craig was so adamant about not registering that he rebuffed warnings by others in his law firm, insisting it was unnecessary and they would be tainted if they did.

“He said it could have consequences for him and, potentially, others on the team if the firm registered as a foreign agent,” said Lawrence Spiegel, general counsel at Skadden Arps, the firm where Mr. Craig worked after leaving the White House. “He said something about the Obama pledge or conflict policy but that if we registered it would bar him and potentially others on the team from going into government for, I think he said, two years.”

Mr. Craig is accused of lying to federal officials who were looking into whether he should have registered his activities in writing and helping roll out a report defending Ukraine’s handling of a prosecution of a former government official.

Prosecutors say he broke the law by working on a strategy for publicizing the report, including personally delivering a copy to a New York Times reporter.

Heather Hunt, former head of the department’s Foreign Agents Registration Act unit, said Mr. Craig and lawyers from Skadden Arps met with her team in October 2013, when he told the investigators he contacted reporters because he felt they were bungling the report’s conclusions.

One of the others involved in the work, former Trump campaign figure Rick Gates, testified last week that Mr. Craig was in fact responsible for suggesting they pitch the report to The New York Times first, saying they would get a fair shake from reporter David Sanger.

Ms. Hunt testified that Mr. Craig didn’t disclose to her team his interactions with Mr. Sanger or another reporter at The Times. nor did he tell them those conversations occurred before the report’s release. She said it was important for her team to know that.

“That was my takeaway from the meeting,” she said. “He [contacted reporters] on his own and not under the request or direction of the government of the Ukraine.”

Defense attorney William Taylor seized on the fact that no notes were taken at the meeting. He said no one can exactly recall what Mr. Craig said at the meeting.

Mr. Taylor cited Ms. Hunt’s grand jury testimony earlier this year in which she testified she didn’t remember which Skadden attorney did most of the talking during the meeting. That contradicted her testimony Monday when she said Mr. Craig spoke for most of the meeting.

“You can’t even tell us who was the main person doing the talking,” he said of Ms. Hunt’s struggles to recall some details from the 2013 meeting.

Ms. Hunt said Skadden’s Ukrainian work drew scrutiny from the Justice Department because of a Los Angeles Times article that included a statement from Mr. Craig.

She said her review uncovered further irregularities including that the Ukraine only paid Skadden a retainer of roughly $12,000 in that country’s currency.

“It was quite a bit of work for $12,000 so that was something we were looking at,” she said, adding her team was trying to learn who was behind the whole effort.

Prosecutors have tried to paint a pattern of obstinance on Mr. Craig’s part, saying he was worried about souring his future chances at government jobs if his work on behalf of Ukraine became known.

Mr. Spiegel recalled a meeting in September 2013, after a Justice Department letter saying the firm needed to register. He said Mr. Craig was “very passionate” about avoiding that outcome, insisting the department was wrong.

Mr. Spiegel said Mr. Craig was so “hot” he wrote an email that contained a litany of inaccuracies about how the firm handled the media rollout of the Ukrainian report. Another letter Mr. Craig wrote to the Justice Department was so pointed that the firm wouldn’t send it.

“We decided the tone of the letter was not the way we as an institution wanted to express ourselves in dealing with the Department of Justice,” Mr. Spiegel said.

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