Prince Nayef bin Abd al-Aziz told the London-based Arabic-language al-Hayat newspaper that any Saudi who might be in Iraq must have entered through a third country.
"These allegations are absolutely baseless and we have no information about any Saudi crossing from our borders into Iraq," Prince Nayef said in an interview published on Saturday.
"We will never allow this to happen and would not be lax with any Saudi who tries to interfere in Iraq's affairs."
"If Saudis did enter Iraq, then they could not have done so through the kingdom's borders. They are likely to have travelled to a third country and then moved to Iraq as a last destination."
US soldiers have faced daily guerrilla ambushes since the end of the war that ousted Saddam Hussein in April and US officials have long suspected that some fighters have come through Iran and Syria.
Last week, US Deputy Secretary of State Richard Armitage said in an interview that some of the people attacking US forces in Iraq are coming into the country from Saudi Arabia as well as Iran and Syria.
Relations between long-time allies Riyadh and Washington have hit their lowest ebb
Relations between long-time allies Riyadh and Washington have hit their lowest ebb after the 11 September 2001 attacks on US cities, which Washington blamed on Saudi-born Usama bin Ladin and the al-Qaida network he is said to lead.
The oil-rich kingdom, which has witnessed a spate of attacks it links to al-Qaida, has cracked down on Muslim fighters since a May bombing in Riyadh killed 35 people, mainly foreigners.