"Yes, they are here, I can confirm that," chief government spokesman Mohamed Hussain Shareef told The Associated Press by telephone from the capital, Male.
"They have gone to one of the islands, but this is very, very secret," he said.
The couple may face bad weather.
"It has been raining heavily the past week and there are predictions of scattered showers," Shareef said. "However, right now there is sunshine."
Cruise, 44, and Holmes, 27, are on one of the Indian Ocean country's 1,192 tiny coral islands after arriving by private jet, the local Haveeru newspaper said, citing witnesses.
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Since their arrival, rumors have gripped the Muslim-majority archipelago of about 350,000 people that a VIP couple was visiting.
An official from the Tourism Department said speculation was swirling on the couple's whereabouts. The official, who spoke on condition of anonymity, said there was a rush for bookings at an underwater restaurant after rumors spread that the duo will have dinner there Tuesday.
"At the moment, we hear that they are cruising on the yacht and that they are expected to visit some of the island resorts — at least one exclusive and expensive one with its underwater restaurant," said another government official, declining to give his name because he was speaking about a private matter.
Ali Siraj, a local journalist in Male, said he heard that the couple was staying on a yacht.
"There are many big boats here, which are like floating resorts and I have heard a rumor that they are staying in one of them," he said.
Shareef said all the resorts were fully booked.
"There is 100 percent occupancy and we are hopeful that we will break the record of 2004," when 615,000 tourists visited. Most resorts damaged by the 2004 tsunami have been refurbished.