David Cameron has said the government "will do everything it can" to evacuate up to 500 Britons left in Libya where violent protests are taking place.
The prime minister said action was being taken "right now" to help British oil workers in remote desert areas, and HMS York was going to the area.
After about 500 Britons left by plane and ship on Thursday, Mr Cameron said those remaining "need to leave now".
The evacuation was earlier criticised as slow, for which the PM apologised.
On Friday morning, Mr Cameron chaired meetings of the National Security Council and Cobra emergency committee, which includes Foreign Secretary William Hague, Defence Secretary Liam Fox, Deputy Prime Minister Nick Clegg and Chief of the Defence Staff Gen Sir David Richards.
The Foreign & Commonwealth Office (FCO) said it had helped about 600 British nationals to leave Libya, approximately 450 directly and the rest by facilitating their departure.
'Quickly and safely'
The Foreign & Commonwealth Office (FCO) has given details of flights returning British nationals to the UK:
- A flight chartered by oil company BP carrying 79 Britons landed at Gatwick airport on Thursday morning
- A later FCO-chartered flight carrying 181 adults and two children, including 113 Britons, landed at 2030 GMT on Thursday
- Another FCO-chartered flight arrived at Gatwick at 0315 GMT on Friday, carrying 130 people including 53 Britons
- A charter flight carrying three Britons arrived at Stansted airport at 0530 GMT
- A charter flight to Gatwick departed Tripoli at 1630 GMT, carrying 34 Britons, 18 Canadians and 27 other nationals
- Another charter flight will depart from Tripoli on Saturday, which is likely to be the last
Some 49 British nationals have departed on a US ferry from Tripoli harbour.
The frigate HMS Cumberland has picked up 207 people including 68 British nationals from Benghazi and is due to arrive in Malta tonight, where evacuees can pick up flights to the UK.
The FCO in London said it had taken more than 1,000 calls in the past 24 hrs from either British nationals wanting to leave Libya, or from family and colleagues in the UK.
Some 25 specialist extra Foreign Office staff have been sent to reinforce teams in Malta and Libya, and the FCO has also helped nationals from about 25 other countries to leave Libya.
A Foreign Office spokesman said: "The security and wellbeing of British nationals is our absolute priority.
"We are doing all we can to get them out of Libya, drawing on both military and commercial assets, as well as working with international partners.
"Our priority is ensuring British nationals can leave Libya as quickly and as safely as soon as possible."
Among the Britons to have been evacuated was a woman who was airlifted with her newborn baby by an Irish government Learjet.
Mr Cameron has apologised for the speed of the government's response and said lessons would be learned from it.
Labour leader Ed Miliband said: "There is a worrying whiff of incompetence about the way this government is handling this issue, and it's become a pattern with this government about the way decisions are made and the way things are handled.
"Frankly, I think Mr Cameron has got to get a grip on the way this Government works."
Latest reports from Tripoli say anti-government protesters have come under heavy gunfire.
Protests in the Libyan capital resumed as demonstrators seeking the overthrow of Libyan leader Muammar Gaddafi emerged from mosques following Friday prayers.
'Opportunity for change'
Mr Cameron discussed Libya on the telephone with US President Barack Obama on Thursday night.
A Downing Street spokesman said: "The prime minister updated the president on his trip to the Middle East, stressing the importance of seizing this moment of opportunity for change in the region.
"The leaders discussed Libya and agreed to work together closely on the swift evacuation of nationals. They also agreed to co-ordinate on possible multilateral measures on Libya, including at the UN Human Rights Council on Monday."
The European Union's High Representative for Foreign Affairs, Baroness Ashton, said the bloc was considering sanctions, including travel bans and asset freezes, to "put as much pressure as possible" on Libya to stop the violence.
Speaking on Friday, Mr Cameron expressed support for an investigation into whether the Libyan regime had committed "war crimes" in its crackdown on anti-government protests.
"The message is very clear: that the violence we have seen is appalling and unacceptable," he said.
He added: "People working for this regime should remember that international justice has a long reach and a long memory and they will be held to account for what they do."
UK nationals wishing to register an interest in flights out of Libya should call 020 7008 0000 from the UK or 021 340 3644/45 from Libya.
The Foreign Office is advising against all but essential travel to Libya.