"Jordan will act with all firmness and force against anyone seeking to undermine its security," he said on a visit to the headquarters of the intelligence services, according to a statement from the royal palace.
"National unity is the weapon we will use to thwart all plans that aim to disrupt stability and cohesion," the king said, adding that the country would not be weakened by "the terrorist acts of traitors".
Earlier, the authorities imposed a media blackout on information about yesterday's attack that killed the five security officers, the official Petra news agency reported.
The blackout came just hours after the government spokesman said a suspect had been arrested following the shooting at the Palestinian refugee camp of Baqaa, north of Amman.
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The five officers had been starting their shift when a gunman struck at their office in the largest of the kingdom's 10 official Palestinian refugee camps.
"Investigations are under way but early indications are that this was an isolated and individual act," government spokesman Mohammed Momani said, announcing the arrest but without identifying the suspect, a Jordanian in his 20s.
There has been no claim of responsibility for the shooting, which came on the first day of the Muslim holy fasting month of Ramadan.
Jordan is a leading member of the US-led coalition fighting the Islamic State group in neighbouring Iraq and Syria, and has been the target of jihadist attacks in the past.