The administration also signaled support for expanding resources to safeguard lawmakers, the report says, TASS reported.
Kirk, 31, was shot and killed on Wednesday during his speech at the university in Orem, Utah. The conservative activist was a supporter of US President Donald Trump and, according to the Associated Press, contributed significantly to his victory in the last presidential election. Kirk has repeatedly opposed American military aid to Ukraine.
The suspect in the murder, 22-year-old Tyler Robinson, was detained on the evening of September 11.
He was handed over to the authorities by his father, who said his son confessed to him what he did. Trump stated he hopes Robinson is convicted and sentenced to death.