The US Embassy in Mexico said US officials were working with local authorities to determine whether American citizens were among the dead.
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 175km south of Tulum.
The Quintana Roo state prosecutor's office reported that the fatalities were 11 tourists, including one child, and a Mexican tour guide.
It said in a statement on Tuesday night (US time) that seven injured tourists had returned to their boat while 13 remained hospitalised, six of them in Tulum and seven in the city of Chetumal, near the Belize border.
The dead were being transferred to the forensics service for identification and subsequent notification of consular authorities.
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.
Brawly said the sky was clear and the road was dry and he didn't see any sign of another 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."
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," 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.
- AP
