A ministry spokesman confirmed that an "assisted departure is currently being carried out" and that further details would be given once all passengers were on board and the ship was in safe waters.
Britain is also planning to temporarily suspend its embassy operations in the troubled north African country, the Foreign Office said.0
The operation is likely to resemble the one used in 2011 during the bloody uprising which ousted dictator Moamer Kadhafi, when a Royal Navy ship evacuated foreigners.
Michael Aron, Britain's ambassador in Tripoli, said Friday he had "reluctantly" decided to leave due to the worsening local fighting.
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Libya has suffered chronic insecurity since Kadhafi's overthrow, with the new government unable to check militias that helped to remove him and facing a growing threat from Islamist groups.
Fighting between the rival militias has forced the closure of Tripoli's international airport, while Islamist groups are battling army special forces in the eastern city of Benghazi.
Between 100 and 300 Britons are thought to be in Libya. Many British consular staff were evacuated last Monday.
"Fighting has intensified in Tripoli, including around the British embassy compounds," a Foreign Office spokesman said.
"In the light of the deteriorating security situation, we are taking steps temporarily to suspend operations at the British embassy in Tripoli after the planned assisted departure of British nationals," he said.
"We advise against all travel to Libya and urge British nationals in Libya to leave through commercially available means.