WASHINGTON — One of two charges against Gregory B. Craig, a former Obama White House official accused of lying to the Justice Department about his work at a prominent law firm on behalf of Ukraine’s government, was dismissed on Tuesday, days before his criminal trial was set to begin.

Judge Amy Berman Jackson of the United States District Court in Washington, D.C., ruled that the government could not prosecute Mr. Craig for making false statements under a foreign lobbying law because the language of the statute was too ambiguous.

But she upheld a second charge under a broader statute that makes it illegal to lie to federal authorities. She rejected arguments by defense lawyers that Mr. Craig could not be held criminally liable for omitting facts in his discussions with the Justice Department, saying “he was obliged to be both truthful and complete.”

Mr. Craig, 74, who served as White House counsel in the first year of the Obama administration, is accused of misleading Justice officials about his work in 2012 for the Ukrainian government, which earned his former law firm, Skadden, Arps, Slate, Meagher & Flom, more than $4.6 million. His trial is scheduled to begin Monday.