A man injured three police officers in Budapest late on Thursday with a knife, one of whom died in a hospital, police said in a statement on Friday.
The suspect was trying to enter a flat in a Budapest apartment block when the police were called, police said.
As the three officers tried to detain him, the man stabbed them and tried to escape to the street, where a fourth officer shot him in the foot, police said.
No further details were available and police were not immediately reachable for comment.
Prime Minister Viktor Orban told state radio on Friday that the government would help the family of the officer who was killed.
Orban did not give any further information about the suspect or the circumstances of the attack.