Federal investigators have been reviewing family text messages as they aim to build a case implicating Democratic Representative Ilhan Omar of conspiring to commit immigration fraud, three people familiar with the matter said this week.

The messages were obtained from a phone that officials seized earlier this year from one of Ms. Omar’s sisters, Sahra Noor, a health care executive and author, according to the three people.

The messages contained information that investigators had used to get a federal judge to authorize homeland security agents to search Ms. Omar’s Washington-area residence on Monday, the three people said. Agents spent hours searching the home of the Minnesota congresswoman and were seen walking away with several boxes of seized items.

The people familiar with the seizure of Ms. Noor’s phone spoke on condition of anonymity to discuss an open criminal investigation that is before a federal grand jury in Minnesota. Federal officials have issued subpoenas in recent days to Ms. Noor and several other people in Ms. Omar’s orbit.

The investigation seeks to determine whether Ms. Omar and her relatives lied or omitted crucial information in immigration paperwork they filed since moving to the United States in the 1990s. They were admitted as refugees after fleeing Somalia’s civil war.

Homeland Security Secretary Markwayne Mullin suggested last month that the investigation could ultimately result in Ms. Omar’s deportation.