The vessel, which was carrying 31 tourists of various nationalities and a 14-member crew, sent out a distress call at 5:30 am (0330 GMT), said a statement from Egypt's Red Sea governorate. An AFP tally confirmed that tourists involved in the incident include nationals from Britain, China, Finland, Poland and Spain.
The "Sea Story" embarked on Sunday on a multi-day diving trip from Port Ghalib near Marsa Alam in the southeast, and had been due to dock on Friday at the town of Hurghada, 200 kilometres (124 miles) north.
Governor Amr Hanafi said that some survivors were rescued by an aircraft, while others were transported to safety aboard a warship. "Intensive search operations are underway in coordination with the navy and the armed forces," Hanafi added in a statement.
Authorities have not confirmed the nationalities of the tourists. Beijing's embassy in Egypt said two of its nationals were "in good health" after being "rescued in the cruise ship sinking accident in the Red Sea", Chinese state media reported. The Finnish foreign ministry confirmed to AFP that one of its nationals is missing. Polish foreign ministry spokesman Pawel Wronski said authorities "have information that two of the tourists may have had Polish citizenship". "That's all we know about them. That's all we can say for now," he told national news agency PAP.
According to a manager of a diving resort close to the rescue operation, one surviving crew member said they were "hit by a wave in the middle of the night, throwing the vessel on its side".
Authorities in the Red Sea capital of Hurghada on Sunday shut down marine activities and the city's port due to "bad weather conditions". But winds around Marsa Alam had remained favourable until Sunday night, the diving manager told AFP, before calming again by morning. By Monday afternoon, it became increasingly "unlikely that the 17 missing would be rescued after 12 hours in the water," he said, requesting anonymity because he was not authorised to speak to the media.
The Red Sea coast is a major tourist destination in Egypt, a country of 105 million that is in the grip of a serious economic crisis. Nationally, the tourism sector employs two million people and generates more than 10 percent of GDP. Dozens of dive boats criss-cross between coral reefs and islands off Egypt's eastern coast every day, where safety regulations are robust but unevenly enforced.