RIYADH (Reuters) - Saudi Arabia said on Tuesday that people it arrested on suspicion of spying this month had direct links to the intelligence services of Iran, its main rival for influence in the Gulf.

"Preliminary investigations, physical evidence which has been collected and statements from the accused in this case have shown a direct link between members of this cell and Iran's intelligence apparatus," said a security spokesman for the Interior Ministry quoted by the official news agency.

He said Iranian intelligence had paid the suspects "in exchange for information and documents about important sites". The investigation is ongoing, he added.

Riyadh announced a week ago it had arrested 16 Saudis, an Iranian and a Lebanese on suspicion of spying.

Iran denied on Sunday that it was linked to spying in Saudi Arabia.

The allegation marks an escalation in friction between the two major oil producers, which face each other across the Gulf.

Sunni Muslim Saudi Arabia and Shi'ite Iran have backed opposing sides in armed conflicts and political struggles across the Middle East, particularly in Syria and in Bahrain.

Riyadh has also accused an unnamed foreign power, which officials have privately named as Iran, of stirring unrest among its own Shi'ite minority, something Tehran has denied.

Saudi Arabia also points to an alleged Iranian plot, announced by United States police in 2011, to assassinate the kingdom's ambassador in Washington. Iran denied that too.

Iran said last week a drunk Saudi diplomat had killed an Iranian national in a car accident. Riyadh has denied the diplomat was drunk.

Members of Saudi Arabia's Shi'ite Muslim minority said the arrested men were from their community and expressed doubt over the veracity of the spying charges.

The 16 Saudis arrested included a pediatric doctor, a university professor and a banker as well as two well-known clerics. Relatives and friends of some of those arrested said they did not believe the men had strong political views.

In a statement issued by 37 Saudi Shi'ite leaders last week, including religious leader Ayatollah Hassan al-Saffar, they accused the government of using the spying charges to escalate sectarian tension to detract public attention from other issues.

Most Saudis follow the rigid Wahhabi school of Sunni Islam that sees Shi'ism as heretical.

(Reporting By Angus McDowall; Editing by Robin Pomeroy)