The 27-year-old man, who has interim name suppression, is on trial at a court martial at Devonport Naval Base in Auckland.
The alleged offences happened in a taxi and an apartment in Canada last year. Court martials have jurisdiction over offences committed overseas.
The Navy able rate denies sexually violating one woman by unlawful sexual connection and two charges of indecently assaulting two other women.
Prosecutor Captain Grace Blanks said the offences happened in Victoria, British Columbia, last August.
"This is a case about a failure of comradeship, a fundamental betrayal of the trust and respect that the men and women who serve in a modern defence force must hold in and for one another," she said.
"It's about a sailor interview who, while serving the NZDF on an international deployment, sexually assaulted three other sailors over a seven-day period."
The women were in a foreign port, had consumed alcohol and were in positions of vulnerability when the assaults occurred, she said.
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"These sailors were his colleagues and his shipmates," she said. "None of them at any point consented to the sexual activity and no reasonable person could believe they were consenting.
"All three of them verbally protested and physically resisted him. They made it clear his advances were unwelcome. Each complainant disclosed the accused's offending, either the same day or the following day, to a friend or colleague. At the time each complainant disclosed it to a friend, none of them were aware that the other complainants had also been assaulted."
One of the women told the court martial a group of Navy members had been shopping, then drinking in Canadian barracks and a downtown restaurant.
She said she left early to go back to the ship and the defendant joined her, groping her in the back of a taxi.
John Van der Zanden, defending, said she could have told the taxi driver what happened.
Fellow defence lawyer Paul Heaslip told the panel of five military members hearing the case that consent would be central to other aspects of their case.
The trial continues.