Moammar Gadhafi's regime is "falling apart and in full retreat," Cameron said.
He said he did not know of Gadhafi's whereabouts.
"The latest information is that the vast majority of Tripoli is now controlled by free Libyan fighters, although fighting continues -- and some of it is extremely fierce," Cameron said after meeting with the British National Security Council to discuss the situation in Libya.
Rebel forces stormed the Libyan capital Sunday, captured three of Gadhafi's sons and engaged in clashes with government forces.
"Gadhafi must stop fighting, without conditions -- and clearly show that he has given up any claim to control Libya," Cameron said.
Gadhafi's fate should be a decision for National Transition Committee Chairman Mustafa Jalil and the new Libyan authorities, the prime minister said.
"The situation in Tripoli is clearly very fluid today and there can be no complacency," Cameron said.
He pledged support for "the will of the Libyan people, which is for an effective transition to a free, democratic and inclusive Libya."
Creating a new government would be "a Libyan-led and Libyan-owned process with broad international support co-ordinated by the [United Nations]," Cameron said, adding he has been in "close contact" with NATO, the Arab League and with Jalil.
Nations must begin working on shipping humanitarian and medical aid to Libya, he said.
"We have already deployed medical supplies close to where they are needed and have now released them to the World Health Organization," Cameron said. "In the coming days, it will be important to make sure the communications networks, the electricity, the power supplies, fuel and water are maintained or repaired where they need to be."
Cameron said the government would establish a British diplomatic presence in Tripoli "as soon as it is safe and practical to do so."
The U.N. Security Council also would work with new Libyan government leaders to give them legal, diplomatic, political and financial support.
Cameron said frozen assets would be released soon.
He thanked British air force troops for their work in the NATO-led airstrikes against Gadhafi targets to protect Libyan citizens.
"Six months ago this country took the difficult decision to commit our military to support the people of Libya," Cameron said. "I said at the time that this action was necessary, legal and right -- and I still believe that today."