The UK wants an investigation into whether the Libyan regime has committed "war crimes" in its crackdown on protests, David Cameron has said.
International justice "had a long reach", the UK prime minister said, and Libyan leader Colonel Gaddafi would be "held to account" for his actions.
He said the UK would push for Libyan assets abroad to be frozen and a travel ban on senior figures in the regime.
Fighting between pro-Gaddafi troops and anti-government forces is continuing.
The UN has said reports suggest the crackdown by troops loyal to the Libyan leader, who has pledged to do whatever it takes to retain his 42-year hold on power, has escalated "alarmingly".
Mr Cameron was speaking after chairing meetings of the National Security Council and the Cobra emergency committee co-ordinating the UK's response to the crisis in Libya.
The government has been criticised for the speed of its response to the crisis and Mr Cameron has apologised to UK citizens in Libya for delays in bringing them home.
The prime minister urged all Britons still in Libya to leave now and said the UK would do "everything it can" to complete its evacuation of UK nationals in Tripoli and elsewhere in the country.
He said six flights evacuating UK nationals had already returned from Libya and more would go in if necessary.
Mr Cameron said his "clear warning" to the Libyan leader was that current violence was "unacceptable".
"I have this very clear message for people in that regime... The world is watching you and the world will hold you to account," he said.
"Britain, through the United Nations, is pressing for asset seizures, for travel bans, for sanctions, for all of the things that we can do to hold those people to account, including investigating for potential crimes against humanity or war crimes or crimes against their people," 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."
The head of the UN's human rights arm Navi Pillay has said thousands of people may have either been killed or injured in recent days as fighting continues in cities across the country.
Nato defence ministers have been meeting to discuss what their next step should be.
The EU's foreign affairs representative, Baroness Ashton, has called for "restrictive measures" against Libya to increase pressure on the regime and to stop the violence.
It has been reported that the UK could also support French-led calls for further sanctions on the Libyan regime including an arms embargo.
Labour leader Ed Miliband said he would back "all necessary action", including sanctions, to "increase the pressure" on the Gaddafi regime.
"We want to see a peaceful transition in Libya away from the current regime to a more democratic future," he told the BBC.