Their ships, Shun-da, registered under the Belizean flag, and Mongolian-flag Yong-Win 18, arrived in Nam Trieu Shipyard for repair on May 13.
The owner, Chinese company Jumbo Sino Development Limited, has apparently abandoned both ships since then.
The crews said they wanted to return to their home countries and claim their backpay,
The maritime authority has provided the crews with food and has asked the shipyard to ensure water and electricity supplies for the ships.
The case was also reported to the national maritime authority for further decision.