Judge Jackson said she was most disturbed by Mr. Patten’s misstatements to the Senate Select Committee on Intelligence about his work in Ukraine and his purchase of the inaugural tickets. She also said his failure to register as a foreign lobbyist for Ukraine was not “a mere technicality” or an oversight, but a serious omission that deprived the American public, members of Congress and policymakers of information necessary to judge the motivations of those who seek to influence them.

“People need the facts for democracy to work,” she said.

Mr. Mueller’s prosecutors uncovered evidence of Mr. Patten’s offenses while investigating Paul Manafort, the former Trump campaign chairman who was recently sentenced to seven and a half years in prison for financial fraud and conspiracy. Mr. Mueller’s team turned the case over to the United States attorney’s office in Washington, D.C.

Although they did not recommend any specific sentence, the prosecutors argued for leniency, saying that Mr. Patten had quickly pleaded guilty and had cooperated with the government in several enforcement matters, including the prosecution of Mr. Manafort. Mr. Patten’s lawyer asked for probation. The charges carried a maximum penalty of five years in prison and a $250,000 fine.

Judge Jackson said she had decided to spare Mr. Patten prison time because he moved quickly to admit his guilt, worked hard to help the special counsel’s investigation and seemed truly remorseful. “You have done everything in your power to make amends,” she said.

Both Mr. Manafort’s and Mr. Patten’s offenses were rooted in their work for pro-Russia billionaires in Ukraine, who paid tens of millions of dollars to western lobbyists and law firms to help shape their political party’s message to the West. Mr. Patten essentially picked up where Mr. Manafort left off in 2014, when Viktor F. Yanukovych, a pro-Russian politician whom Mr. Manafort helped elevate to Ukraine’s presidency, was forced from power and fled to Moscow.