The F.B.I. said on Thursday that it was investigating the shooting of two Indian immigrants by a white man who leveled ethnic slurs at them and questioned their immigration status before he opened fire at a Kansas bar as a hate crime.

The suspect, Adam W. Purinton, was thrown out of Austins Bar and Grill in Olathe, Kan., last Wednesday after verbally harassing the two Indian men, Srinivas Kuchibhotla and Alok Madasani, and suggesting they did not belong in the United States, the authorities said.

He returned to the bar with a gun a short time later and shot both men as they sat on its outdoor patio, killing Mr. Kuchibhotla and injuring Mr. Madasani, the authorities said. Ian Grillot, another bar patron, was also shot and injured as he tried to stop Mr. Purinton from fleeing the scene.

Mr. Purinton was charged last week with premeditated first-degree murder and two counts of attempted premeditated first-degree murder. The Kansas City division of the F.B.I. said on Tuesday that federal authorities were also investigating the shootings as a hate crime. The move was not unexpected given the nature of the shooting.

“Based upon the initial investigative activity, the F.B.I., in conjunction with the U.S. Attorney’s Office and the Justice Department’s Civil Rights Division, is investigating this incident as a…