He later added that police have "no indications yet" that Metsos had left the island or crossed into its northern Turkish sector.
Police are monitoring all exit points from the Mediterranean island and the line dividing the Turkish-held north from the Greek Cypriot south.
The hotel's staff said Metsos was last seen at the reception on Tuesday evening and had paid for two weeks in advance with a credit card.
Metsos, a 54-year-old who says he is Canadian, was arrested at Larnaca airport on Tuesday after immigration officers discovered his name on a stop list.
He was the only one of the 11 suspects, who have been accused of acting as agents for a foreign government, to be detained outside of the US.
An extradition hearing for Metsos was scheduled for July 29.
Police told the court in Larnaca that Metsos was wanted in the United States for spying on behalf of Russia and for laundering $40,000.
Michalis Papathanasiou, his lawyer, told the Reuters news agency he had had no contact with the suspect on Wednesday.
On Monday, US authorities announced the arrest of 10 "deep-cover" suspects accused of infiltrating policymaking circles and reporting back to Russia.
The suspects were accused of seeking information on issues ranging from nuclear weapons research to the global gold market and CIA job applicants, according to US prosecutors.
Moscow appeared to soften its initially angry reponse to the allegations on Wednesday, saying it did not believe that the arrest would harm relations with Washington.
"We expect that the incident involving the arrest in the United States of a group of people suspected of spying for Russia will not negatively affect Russian-US relations," a foreign ministry official said on condition of anonymity.
Vladimir Putin, the Russian prime minister, and Sergei Lavrov, the foreign minister, both reacted angrily when the claims were originally put before them, with the latter suggesting that the timing was suspicious.
Dmitry Medvedev, the Russian president, visited Barack Obama, his US counterpart, in Washington last week as the the two nations made an effort to "reset" relations strained since Russia's war in Georgia in 2008.