The delegation from the Klondiker, Rotalia, was representing 26 other crew members who have taken the industrial action over a claim that they have not been paid for nearly three years by their Bulgarian state company.
Two officers from the ship owned by Okeanski Ribolvova - which also has two other ships in detention in British waters - went to the embassy with Joan Walley, Labour's shipping spokeswoman, and Jimmy Knapp, leader of the Rail, Maritime and Transport union in an effort to break the deadlock.
After a frank two-and-a-half hour meeting, the ambassador, Stefan Tafrov, and representatives from the company agreed to further meetings at the embassy in an attempt to reach a settlement.
Mr Tafrov guaranteed that the striking seamen would not face legal action if they returned to Bulgaria, as had been implicitly threatened.
The seamen, whose ship was detained at Lerwick by the Marine Safety Agency in October because of a catalogue of defects, also took a petition to Downing Street.
They have been unable to buy food and have been dependent on handouts from islanders.
The ships, nicknamed Klon dikers after the 19th-century Canadian gold-diggers, are a vital part of Britain's fishing industry, processing more than half of Scotland's annual mackerel and herring catch for export to the Continent and the Far East. The vessels, mainly from Bulgaria, Latvia, Lithuania, Estonia and Russia, sail into the North Sea and Atlantic waters each winter and summer at the start of the mackerel and herring seasons. At the height of the season, there are more than 100 vessels anchored off Shetland and the west coast.
Although the crews enjoy the support of local people, the Klondike fleet has recently been criticised over poor safety standards.
Last October, a Russian factory ship, the Pionersk, ran aground and broke up off Shetland, spilling 100 tonnes of oil.Reuse content