Devonport-based amphibious assault ship HMS Albion has left Plymouth for the Mediterranean.
The ship is taking part in exercise Operation Cougar which the Ministry of Defence (MoD) says has been planned for the past two years.
HMS Sutherland and troops from 40 Commando Royal Marines are also leaving as part of the same deployment.
The MoD denied it was linked to the situation in Libya, but said the ships could provide humanitarian relief.
The Devonport ships taking part in Operation Cougar are expected to be away for six months.
Families gathered at the traditional collecting place of Devil's Point in Plymouth to wave farewell to the crew as HMS Albion sailed out of Devonport.
The MoD said the newly-formed Response Force Task Group (RFTG) would be taking part in multi-national amphibious exercises in the Mediterranean and later in the Indian Ocean.
HMS Albion, Type 23 frigate HMS Sutherland, and the Royal Fleet Auxiliary Cardigan Bay were sailing as the lead element of the RFTG, which is held at "very high readiness" to respond to "unexpected global events".
HMS Albion, a landing platform dock capable of carrying more than 600 people, left Devonport just after 0800 BST.
Task group commander, Cmdr John Kingwell, said: "Cougar 11 is an important opportunity to develop international inter-operability and build long-term defence relationships, and for the RFTG to demonstrate operational contingent capability."