Federal prosecutors filed a felony charge earlier this year against a man who briefly served as a bodyguard for Representative Ilhan Omar in what his lawyer described as an unusual gambit to obtain incriminating information about the lawmaker.

The case against the bodyguard, Abdullahi Mohamed, who was accused of lying to a government official under oath, provides new insight into the Justice Department’s efforts to build a criminal case against Ms. Omar, a Minnesota Democrat who last week won a fifth term in Congress.

Federal prosecutors are reviewing Ms. Omar’s family immigration history as part of a sprawling criminal investigation that focuses in part on whether she entered into a sham marriage to help a man suspected of being her brother obtain a green card. Mr. Mohamed’s case reveals that investigators have simultaneously been scrutinizing the lawmaker’s financial dealings.

The immigration case burst into the open last month after federal agents searched Ms. Omar’s Washington home and issued subpoenas to compel several people close to her to testify before a grand jury. Ms. Omar has denied wrongdoing and called the investigation a form of political persecution by President Trump, who has long denigrated her and fellow Somali immigrants in racist and xenophobic terms.

Mr. Mohamed’s lawyer, Bruce Rivers, said that prosecutors spent months trying to turn the bodyguard into an informant to bolster their case against Ms. Omar. In a move he described as shocking, Mr. Rivers said that prosecutors repeatedly told him and Mr. Mohamed that the investigation into Ms. Omar was “100 percent being run by 1600 Pennsylvania Ave.,” the address of the White House.