“We would ask Jeremy Hunt to apply some pressure on the Italian authorities to accept 47 people on board and allow the crew to leave.”
Head of mission Kim Heaton-Heather, 37, originally from Brighton, is heading the mission.
Also on board are chief engineer Jon Stone, a 32-year-old former Navy serviceman from Lincoln, and bosun Dan Bebawi, 39, formerly a car mechanic in Nottingham.
The crew said they were not granted permission to land by Malta before the Italian coast guard said on Friday they could shelter in its waters.
The Foreign Office said it is tackling “irregular migration” with a “whole of route” approach that emphasises interventions at every stage of their journeys.
“This includes the well-established principle that rescued migrants should be able to disembark at the nearest safe port,” the spokeswoman added.
Sicilians have offered their support and three United Nations agencies have appealed to Italy to allow the migrants off the ship.
And while the mayors of Naples and Palermo have offered their ports, the jurisdiction lies with national authorities.