The orders apply to guards patrolling the southern border with Yemen as well as the northern frontier with Iraq, Major General Mohammed al-Ghamdi told AFP.
Senior commander General Odah al-Balawi was among the three border guards killed in the January 5 clash with four Saudi infiltrators, two of whom blew themselves up.
“After that, we will not negotiate with anyone,” Ghamdi said.
“We will shoot them directly without any warning, without any negotiation.”
He said security officers on the Iraqi side had been told of the new orders.
No group has claimed responsibility for the border clash but Saudi Arabia is among Arab countries taking part in US-led air strikes against the Islamic State jihadist group in Syria, raising concerns about possible retaliation inside the kingdom.
Ghamdi said he did not know if the “terrorists” belonged to IS, but they came from the direction of Iraq and tried to enter through an official crossing in the Arar region.
Officers tried to stop the infiltrators after spotting them on infra-red cameras, shooting two of them dead.
Thousands of riyals (dollars) were found on their bodies, suggesting they had hoped to reach a target elsewhere in the kingdom, Ghamdi added.
Security officers later arrested seven suspected associates of the four infiltrators.
For security reasons, Ghamdi declined to say how many officers are stationed on the frontier.
Last September, the kingdom inaugurated the first stage of a protective fence and surveillance system stretching for about 900 kilometres (560 miles) along the northern desert frontier.
“It’s very high-tech,” Ghamdi said.
The shoot on sight order also applies to the southern border with Yemen, where Al-Qaeda in the Arabian Peninsula has established a major presence amid deepening instability. -AFP