Authorities told WOAI, San Antonio, the agent was in uniform and on duty Wednesday when he allegedly encountered a woman and two 14-year-old girls trying to enter the country in Hidalgo County.
The agent, whose name was not provided, allegedly cut the woman with a knife and raped one of the teenagers before taking the other girl to his apartment and locking her inside, the radio station said.
WOAI said the agent went back to work to finish his shift, then returned home where he allegedly raped the girl he was holding.
The Customs and Border Protection agency said in a statement Mission police had entered the agent's home.
"Upon entry, Mission PD ..., together with CBP and other law enforcement entities, found the agent deceased and discovered the third female," the agency said in the statement.
In a statement, the FBI confirmed its agents in McAllen were investigating "the kidnapping and assault of three undocumented female aliens" in the Rio Grande Valley.
Authorities had no further comment on the case, WOAI said.