The US claims Iran was involved in the Khobar attack
The US has "a major problem" with Iran over its "support for terrorist activities against the United States and in the Middle East," she said in comments published on Thursday in al-Hayat newspaper.
She restated allegations that Iran was involved in a bomb attack which killed 19 servicemen at a US military complex in the Saudi city of Khobar in 1996.
"When we questioned those who carried out the explosion in the Khobar complex, they clearly mentioned training and finance provided by Iran," she told the Arabic daily.
The US issued indictments against 14 suspects - 13 Saudis and one Lebanese - in June this year.
The charges claimed the alleged bombers were trained in parts of Iran and Lebanon controlled by Hezbollah.
In announcing the indictments, US Attorney-General John Ashcroft said factions within the Iranian regime had "inspired, supported and supervised" Saudi Islamic militants to carry out the attack.
Tanker row
Ms Rice's statements came the day after Iranian government officials, in a report on state television, accused US forces of attacking an Iranian-registered Saudi oil tanker in the Gulf.
The report said two US frigates intercepted the ship and two of the tanker's crew were injured when US forces on speedboats "opened fire".
A foreign ministry official statement quoted called the incident a "vile act of aggression".
The television report quoted Swiss ambassador Tim Guldimann, whose country represents US interests in Iran, saying that the American troops had mistaken the tanker for an Iraqi vessel smuggling oil.
Oil sanctions have been imposed on Iraq by the United Nations since Iraq's invasion of Kuwait in 1990 and US forces often intercept tankers accused of smuggling Iraqi oil.
But Iran's oil ministry said the tanker was carrying products between Saudi Arabia and Iran.
Severed ties
Iran and the United States severed diplomatic ties after the 1979 Islamic revolution and the takeover of the US embassy in Tehran.
But US-Iranian relations showed signs of thawing under former US President Bill Clinton when the reformist President Mohammed Khatami was elected in 1997.
The Clinton administration did not bring charges against anyone implicated in the Khobar bombing, despite a five year inquiry in which the BBC's Middle East analyst Roger Hardy says the then head of the FBI, Louis Freeh, became convinced of Iranian involvement.
The Bush administration has continued to accuse Iran of supporting terrorism, maintaining trade sanctions against the country and vetoing its application to join the World Trade Organisation.