Speaking in an interview with Saudi daily Okaz Tuesday, al-Sabah said Kuwait and Saudi Arabia were cooperating closely to uproot terrorism, which is sweeping their countries.
"Terrorism has no identity or belonging ... It is an international trend that necessitates cooperation from all sides in order to eradicate it," al-Sabah said.
He said the Kuwaiti government is determined to hunt down the terrorists and eliminate them.
Four gunmen were killed, three wounded and another three captured in a clash with police Monday south of Kuwait City. Among those captured was the group's leader, Amer Khalid al-Onazi.
"I don't know where these terrorists came from ... Three of them are without identity and some are Saudis," he said.
He said the arms and ammunition seized from the gunmen and discovered in certain parts of Kuwait date back to the Iraqi invasion of the oil-rich emirate.