In a statement on Monday, Mr. Booker said that he was concerned that Ms. McFarland might have given “false testimony” in her answers.

“If this is the case, this is an alarming development, and another example of a pattern of deception on the part of Trump’s closest associates regarding their connections and communications to Russian government officials,” he said.

Court documents released on Friday, along with Mr. Flynn’s guilty plea, indicate that senior members of Mr. Trump’s transition team were well aware of his discussions with the Russian ambassador about the Obama administration’s sanctions. Mr. Flynn talked to Mr. Kislyak by phone on Dec. 29, the day the sanctions took effect, and several days later.

In her email to another transition official hours before the first phone call, Ms. McFarland described President Barack Obama’s decision to expel 35 Russian diplomats as a last-minute attempt to discredit Mr. Trump’s victory, box him in diplomatically and provoke him into a potentially politically damaging statement in Russia’s defense.

“General Flynn is talking to the Russian ambassador this evening,” she wrote.

She also wrote: “If there is a tit-for-tat escalation, Trump will have difficulty improving relations with Russia which has just thrown U.S.A. election to him.” A White House lawyer said on Friday that Ms. McFarland did not mean Russia had tipped the election, only that Democrats were portraying it that way.

Court documents state that Mr. Flynn discussed what he should tell Mr. Kislyak with another transition official beforehand and briefed that person afterward. The court documents do not identify that official, who was with other senior members of the transition team at Mr. Trump’s Mar-a-Lago resort in Palm Beach, Fla. White House officials said on Friday that they believed that the official was Ms. McFarland, but that information has not been confirmed.

During their follow-up call, Mr. Kislyak informed Mr. Flynn that Russia would not retaliate immediately for the sanctions — a surprise to many foreign policy experts. Mr. Flynn then briefed senior transition team members about his discussions with Mr. Kislyak, the records show.

Ms. McFarland worked so closely with Mr. Flynn on the transition team that her colleagues sometimes referred to her as his “brain.”