The vessel says that when it moved to meet the Libyan coast guard, migrants threatened the crew, pushing them and making "cut your throat" gestures.
Italy intervened in a migrant rescue by a private Italian ship this week after migrants reacted to attempts to hand the operation over to Libyan authorities by threatening the crew, the vessel said.
The Vos Thalassa took 67 migrants, including six children, onboard on Sunday after responding to a distress call off the Libyan coast.
Several local and international media reports said the ship was denied permission to dock in Italian ports because of the migrants, marking the first time the government had turned away an Italian vessel.
The migrants were then handed over to the Italian coast guard, the reports said.
However, international shipping company Vroon, which operates Vos Thalassa, an oil rig supply vessel, told Euronews that the ship "never requested to enter an Italian port or even Italian territorial waters."
Vroon said that when the vessel turned to meet with the Libyan coast guard to transfer the migrants, they "started to threaten the crew, surrounding and pushing them and making ‘cut your throat’ gestures."
"Because of these threats the vessel returned to its position and reported this situation to the MRCC [Maritime Rescue Coordination Centre] in Rome."
The shipping company said being "severely outnumbered on board a merchant vessel by an angry crowd that has very little to lose is very frightening".
"We are very proud of the professionalism of our crew in these very challenging circumstances."
The Italian coast guard echoed the claims in a statement to Euronews, saying the commander of the ship “reported a situation of serious danger for the security of the ship and its crew... caused by attitudes threatening the crew by some migrants”.
It said that after picking up the migrants on Monday evening, it was “identifying those responsible for the disturbances”.
Italy’s Transport Minister Danilo Toninelli said on Twitter that he was proud of the Italian coast guard for taking the migrants “who were endangering the life of the Italian cruiser Vos Thalassa.”
“Now onwards with investigations to punish troublemakers," he wrote.
News of the incident comes as Italy continues to clamp down on migrant arrivals.
In a recent interview with an Italian radio station, Interior Minister Matteo Salvini said the country’s ports would “be closed all summer” to NGOs transporting migrants and that the ban would include "the furnishing of fuel” to their vessels.
Last month, Libya, with the backing of Italy and the European Union, quietly took ownership of a large area of the sea migrant route into Europe for search and rescue operations, in a move critics argue will block asylum seekers from reaching safety.
Prior to the change, there was no official search and rescue zone in the area, with the coordination of responses to migrant crises there typically falling to Italy.
While migrants should be transported to safety under international law, search and rescue NGOs told Euronews that they were now being taken back to Libya, where they said there are no safe ports.
Vroon said it was unable to comment on the Italian government's policy on migration, an issue it described as a "very sad and humanitarian drama".
"The duty to save people in distress is a universal obligation, valid throughout the world... Our vessels are in very close contact with the MRCC in Rome," it said.
More than 640,000 migrants have landed on Italian shores since 2014, but numbers have fallen dramatically in the past year, with around 17,000 people arriving so far in 2018.