There was no immediate indication of any deadline.
Yemen's official news agency earlier quoted an official from the interior ministry as saying the tourists were in "very good health".
Yemen deployed troops on Monday to try to free the tourists who were captured in the east of the country on Sunday.
Scores of holidaymakers and foreigners working in Yemen have been kidnapped over the past decade by tribesmen demanding better schools, roads and services, or the release of prisoners. Most hostages have been released unharmed.
Ali Abdullah Saleh, the Yemeni president, has vowed to crack down on such abductions. The latest kidnappings coincide with campaigning for the September 20 presidential and municipal elections.
Yemeni security sources said members of the same tribe had taken hostage - and later released - five German tourists last year.
Impoverished Yemen hopes to boost its tourism, but attacks by al-Qaeda-linked fighters and kidnappings by disgruntled tribesmen have scared off many travellers.
Yemen has executed at least two convicted kidnappers so far this year.