A total of 345 migrants, mainly women and children, had been plucked from a boat in trouble off the coast of Cyprus on Thursday by a Salamis Cruise Lines ship, according to the company and Cypriot authorities.
Some 700 paying passengers disembarked from the 157-metre (515-foot) liner at the port of Limassol, police said, but only 65 of those rescued at sea left the ship.
The others refused to budge, the shipping company said.
"We were supposed to sail at 10:30 tonight (1930 GMT on Thursday), unfortunately these people want to negotiate," Kikis Vassiliou, managing director of Salamis Cruise Lines, told reporters. "They want us to send them to Italy."
"We did our utmost to save their lives, to give them food, support and now they want to destroy this company," he added, speaking of several hundred thousands of euros (dollars) in losses.
"There is no responsible person to negotiate and to explain the situation," he said.
At 4:00 am (0100 GMT) on Friday, negotiations were continuing, with doctors, nurses, civil defence and Red Cross workers on hand.
The 65 refugees who willingly left the ship were bussed to the Kokkinotrimithia camp not far from Nicosia.
Meanwhile 300 Russian passengers, who had been due to continue their cruise to Haifa, Israel, had their journey cancelled and were put up in Limassol.