The prime minister is presiding over efforts to rescue the British nationals remaining in Libya, after returning from his trip to the Middle East.
David Cameron chaired a national security council meeting before holding a meeting of Cobra, the Cabinet's emergency committee.
A second Royal Navy ship, HMS York, has been dispatched to international waters off Libya as a result.
Mr Cameron returned from his Middle East trip yesterday after being let down by his Cabinet, in particular by foreign secretary William Hague. The PM was forced to say he was "incredibly sorry" yesterday for the difficulties encountered in evacuating Britons.
Yesterday over 350 British nationals were finally evacuated from five flights departing Tripoli. That followed an initial delay in arranging them and then further problems caused by technical faults and airlines refusing to make the trip.
By Friday lunchtime Mr Cameron was attempting to present an image of a government completely in control of the situation.
"We will do everything we can today and tomorrow to help those people and planning is under way to do just that," he said.
"In the last 24 hours there have been six flights that have left Libya and that is good, and there will be more on the way if necessary.
"HMS Cumberland has now come out of Benghazi, bringing many, many British citizens out of Benghazi and we have also helped citizens of 25 other countries. I have also asked HMS York to go into the area and help out if necessary.
"But I would say that people do need to leave now and that is the message that I give very strongly to British citizens in Libya."
HMS Cumberland sailed from Benghazi with 207 passengers on board, around 68 of whom were British.
Passengers boarded a further charter flight this morning in Tripoli. It remained on the runway for several hours, however, only departing at 16:30. Thirty-four Britons, 18 Canadians and 27 nationals were on board.
The security situation at the airport has deteriorated in recent hours, raising questions about how easy it will be for the remaining Britons to escape from the fighting. One further charter flight will depart from Tripoli on Saturday.
A US ferry with 49 Brits on board finally left Tripoli harbour, after enduring over a day of delays because of bad weather conditions.
"The security and wellbeing of British nationals is our absolute priority," the Foreign Office said in a statement issued this afternoon.
"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."
Concerns remain about up to 170 British oil workers trapped in remote camps in the Libyan desert, however.
A special forces unit is believed to be in preparation for a rescue attempt, although commanders will be reluctant to commit to the move until the last possible moment.
Mr Cameron added: "For those in the desert, we will do everything we can and we are active on that right now to help get you out."
Around 50 other British nationals are believed to still be in the capital, Tripoli, where Muammar Gaddafi continues to fight deepening resistance to his rule.
He has already lost control of much of the west of Libya but remained defiant, addressing a crowd of supporters in Green Square as dusk fell.
Britain and the US are set to lead efforts to pursue "possible multilateral measures" on Libya, including at the UN human rights council on Monday, Downing Street said.
Asset seizures, travel bans, sanctions and investigations into crimes against humanity are all being pressed by Britain.
"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," Mr Cameron warned.
Sky News alleged that Foreign Office officials in Tripoli had offered airport authorities bribes in order to secure the departure of British citizens.
The Foreign Office categorically denied the claim, however, insisting that its payments were for services such as aircraft handling.
"In the current situation, these fees have increased," a spokesperson said.
"Like those countries and carriers, we have had to pay them - the alternative being to leave hundreds of British nationals stranded in Tripoli. Paying charges levied by the authorities at a foreign airport is not bribery."
Labour leader Ed Miliband voiced his own criticism of the government's handling of the situation yesterday, when he said that ministers had "taken their eye off the ball".
"I don't think the Conservative-led government was sufficiently focused on this," he added.
Britain's struggles over a few hundred of its citizens are nothing compared to the much larger challenges faced by many other countries.
Beijing is attempting to extricate its 30,000 citizens from Libya. There are 60,000 Bangladeshis and 30,000 Filipinos in the country, the AFP news agency reported.
It said Germany had sent three warships, Russia three planes and Greece three troop transport aircraft to rescue their respective citizens.