The US special envoy to the Middle East has had talks in Tripoli with Libyan leader Colonel Gaddafi.
Burns has played a key role in talks with the Libyans
William Burns is the first high-ranking US official to visit Libya in more than 30 years.
The visit marks improved US-Libya relations after Tripoli's decision in December to scrap its WMD programmes.
Officials said Mr Burns had handed over a letter from US President Bush which had dealt with bilateral relations and the international situation.
In Washington, US Secretary of State Colin Powell said the two countries were moving ahead with the political roadmap which had been laid out with the Libyans after they agreed to give up their weapons.
Mr Burns was expected to discuss further moves toward the lifting of American sanctions on Libya and the restoration of normal relations.
Gaddafi has been making peace moves
Until last December, the US maintained a stranglehold on Libya economy with a set of strict trade sanctions, says the BBC's Greg Morsbach.
As US assistant secretary of state, Mr Burns has played a leading part in negotiations with the Libyans - earlier over the Lockerbie bombing and also at last month's London talks, our correspondent says.
Libya has accepted responsibility for the 1988 bombing of a US airliner over Lockerbie in Scotland, which killed 270 people.
On Monday, Colonel Gaddafi's son told reporters that British Prime Minister Tony Blair would also visit Libya this week.
However, the visit has not been officially confirmed by Downing Street, which says it will not comment on Mr Blair's travel plans for security reasons.