"We are expecting there to be a significant event in Riyadh," said a spokesman in London for the Committee for the Defence of Legitimate Rights (CDLR), a fundamentalist group opposed to the Saudi government.
Radical activists have frequently predicted trouble in the past only to see their prognostications come to nothing. But sources close to the Islamic opposition said the militants had orchestrated a strategy to embarrass the government, sending more than 500 faxes to supporters in Saudi Arabia over the past few weeks.
The CDLR spokesman said his group was calling on the faithful simply to congregate and to hold a vigil at mosques in each city, "just to read the Koran and to show their anger". It had designated the King Abdul Aziz mosque in Riyadh as the focal point for the demonstration. The mosque stands in an area inhabited by expatriates near the Khozama hotel, which is used by visiting business people.
Under Saudi law there is no freedom of assembly and the government could use the security forces to break up any illegal gathering. But is is difficult to see how the police could intervene within the precincts of a mosque without offending worshippers.
The CDLR has chosen today because the annual pilgrimage to Mecca is drawing near, thereby focusing attention in the Muslim world upon the kingdom. The move comes as the US is seeking to strengthen its presence in the Gulf in pursuit of the Clinton administration's strategy of "dual containment" towards Iraq and Iran.
Mr Perry's visit follows a trip to the region by the US Secretary of State, Warren Christopher. The US intends to step up its naval and air enforcement of sanctions on Iraq, which is reckoned to be selling $800m (£500m) worth of oil through smuggling.
It also wants to keep up pressure on Iran, which recently deployed Hawk anti-aircraft missiles near the Straits of Hormuz.