Saudi Arabia was stunned by the devastating Riyadh car bombing
The Saudi Crown Prince, Abdullah bin Abdulaziz, has urged Saudis not to protect extremists in what he described as the "decisive battle" against terrorism.
His comments came a day after the US and Britain warned air travellers of a possible terror attack in Saudi Arabia and British Airways cancelled its flights to the kingdom.
"Our noble Saudi people are engaged in a decisive battle against the forces of evil and destruction, represented in the oppressive deviant group of terrorists," Prince Abdullah told security officials.
He warned that those who helped "terrorists" would be considered "terrorists" themselves and would be punished accordingly.
"In the struggle between forces of good and forces of evil, there is no room for being neutral or hesitant," he said.
BA's decision on Wednesday to cancel flights to Saudi Arabia followed intelligence reports of a specific threat to British airlines flying in or out of Riyadh international airport.
The airline has suspended all flights to the kingdom until further notice.
Later, the US State Department renewed an existing warning to US citizens to avoid non-essential travel to the kingdom.
The Saudi Interior Minister, Prince Nayef bin Abdulaziz, denied that the government had received information about any attempt to attack commerical aircraft in Riyadh.
But both the UK and US said their intelligence had come from the Saudi authorities.
The BBC's Kim Ghattas, who is in the region, says that, three months after 35 people died in a car bombing in Riyadh, there is a fear that Islamic militants are preparing more attacks against western targets.
Since the May attack Saudi Arabia has cracked down on Islamist groups with suspected links to Osama Bin Laden's al-Qaeda network, arresting scores of suspects.
The clashes have left 16 suspects and 11 policemen dead.
On Tuesday, Saudi police carried out a major raid in Riyadh's al-Suwaidi district. Four Saudi policemen and one suspected militant died in the shoot-out.
Some of the men targeted in the raid reportedly managed to escape.
It is these men who are thought to be preparing an attack against British targets.
After having been criticised by the US for not doing enough in the war against terrorism, Saudi Arabia is now determined to deal with the Islamic militants.
It sees them as a threat to the security and stability of the kingdom itself, our correspondent says.
A Saudi security official said that the authorities were still on the trail of suspected militants linked to al-Qaeda.
"We will continue to uproot evil terrorists and expect to
accomplish something soon," he told Reuters news agency.
Passengers seeking information on BA flights to Saudi Arabia can ring the airline's main number on: 0870 8509850.