Video images from the scene showed the bus on its side in vegetation off the two-lane highway, with some survivors lying on the pavement and others walking around.
Miami-based Royal Caribbean Cruises said in a statement that passengers from two of its ships, the Celebrity Equinox and Serenade of the Seas, were involved in the crash. The company expressed its sympathies and said it was assisting with medical care and transportation.
The US Embassy in Mexico said officials were working with local authorities.
Mr Martin said investigators were working to determine the cause of the crash, which occurred as the bus was on its way to the ruins at Chacchoben, about 110 miles (175 kilometres) south of Tulum.
Chris Brawley, a passenger on the Serenade of Seas, was on a bus headed to the same Mayan ruins when they came on the scene minutes after the accident.
It was shortly after 9am and a convoy of buses from the cruise port at Mahahual was headed to Chacchoben, he said. They had been on the road for about 35 to 40 minutes before the accident.
Mr Brawly said the sky was clear and the road was dry and he didn't see any sign of any other vehicle being involved in the crash, which happened on a narrow, two-lane road with no shoulder or guardrail.
He said he did not see the crash, but “the bus clearly lost control somehow as there were swerve marks all over the road surface.”
Mr Brawley, of Haslet, Texas, said his ship departed Fort Lauderdale, Florida, on Friday for a seven-day cruise. They were in Roatan, Honduras, on Monday and were scheduled to be in Cozumel on Wednesday.
Michael Schuenemeyer, a minister from Cleveland, was on another bus that passed the crash about an hour later.
Tow trucks were lifting up the bus when they passed by, he said. “It was in pretty sad shape,” Mr Schuenemeyer said.
Costa Maya Mahahual, the bus company involved, said in a statement that in addition to the tourists, a guide and driver were aboard the bus.
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