Former US President Barack Obama has warned of a "political crisis of the sort that we haven't seen before" in the wake of the killing of Charlie Kirk.

At an event in Pennsylvania on Tuesday, Obama said he did not know Kirk and disagreed with many of his views, but called the killing "horrific and a tragedy".

He criticised Donald Trump's remarks towards his political opponents and pointed to previous Republican presidents who, he said, emphasised national unity in moments of high tension, US media report.

In response, the White House called Obama the "architect of modern political division".

Kirk, 31, died of a single gunshot wound while speaking at Utah Valley University in Orem on 10 September.