In arguing that she posed a flight risk and should be jailed pending trial, prosecutors asserted that Ms. Butina, 29, only struck up a relationship with a Republican operative, Paul Erickson, 56, to further her work as a Russian agent. They also said she once offered sex in exchange for a job with an unnamed special interest group.

Citing the evidence presented by prosecutors, Magistrate Judge Deborah A. Robinson of Federal District Court in Washington ordered Ms. Butina held in jail.

But both of the government’s claims about Ms. Butina’s behavior are false, her lawyers said Friday. They said that they had pressed prosecutors for evidence supporting their claim that she had offered sex for a job and that the government put off answering them.

When prosecutors eventually revealed the basis for the allegation, Ms. Butina’s lawyers said, it turned out to be an “innocuous three-year-old text exchange” between Ms. Butina and a longtime friend who worked for her gun-rights organization — and who had just helped her renew her car insurance.

During the conversation, which took place while both were in Russia, Ms. Butina — who, her lawyers said, was friends with the man’s wife and considered him to be like a brother — jokingly offered sex for the favor. At no point during the conversation did Ms. Butina seek a job, they said, and the only special interest organization mentioned was the one she had founded.