The governor of the southern Saudi Arabian province of Jizan has said no leniency will be shown from the authorities in the country's clampdown on terrorists.
Saudi authorities have intensified their search for al-Qaeda suspects
Prince Muhammad Ibn Nasser was speaking a day after three suspected al-Qaeda militants and a policeman were killed in a shootout in Jizan.
Prince Muhammad also called on neighbouring Yemen - where guns are openly available - to take measures to stop weapons being smuggled into Saudi Arabia.
Meanwhile, the Saudi ambassador to the United States has said his country tried to act against terrorist suspects before the September 11 attacks on the United States, but met resistance from US state department officials.
Prince Bandar bin Sultan said the officials had labelled the suspects "dissidents" and criticised the Saudi authorities from treating them badly.
Fifteen of the 19 hijackers involved in the attacks on New York and Washington were Saudi nationals.
Tuesday's gun battle occurred at a housing compound at King Fahd hospital in Jizan.
Saudi officials said police had tried to arrest five armed militants, who had barricaded themselves in a hospital apartment and had apparently taken hostages.
"They were intending to carry out terrorist operations and were armed with machine guns and hand grenades," an interior ministry statement said. "They were asked to surrender but started firing at security forces."
The officials said three gunmen had been killed and two had surrendered.
Saudi sources have told the BBC that one of those arrested is a leading al-Qaeda suspect.
They have named him as Sultan Jubran al-Qahtani, a 29-year-old Saudi who is on the "most wanted" list of the US Federal Bureau of Investigation.
He is also one of 19 men who have been sought by the Saudi authorities in connection with the bomb attacks in the capital, Riyadh, in May.
Since those attacks, Saudi police have been engaged in a campaign against Islamic militants.
It is estimated that more than 200 people have been arrested and a number of others killed in police raids against suspected militants.