A US congressional delegation has held talks with officials in Libya in the first such mission since Colonel Muammar Gaddafi took power.
The US officials hope to visit a former weapons site
The talks follow Libya's diplomatic overtures to the West, including a pledge to halt banned arms development.
US delegation leader and Republican Representative Curt Weldon hailed the visit as "historic".
Correspondents say the trip reflects a growing momentum towards healing the bitter rift between US and Libya.
The group joined Representative Tom Lantos, who became the first elected US official to set foot in Libya for 38 years when he arrived on Saturday.
Mr Weldon, a senior member of the House Armed Services Committee, told French news agency AFP he expected sanctions to be lifted and official ties resumed.
No US congressman has visited Libya since Mr Gaddafi took power
"This visit is historic, we are seeking the establishment of official ties between
the two countries," he said.
But Mr Weldon also stressed that he did not officially represent the US administration and that it would be up to the US president and secretary of state to decide on a resumption of ties.
Libya wants a speedy normalisation of relations with the US, but there is no sign yet that Washington is prepared to lift sanctions against the north African state.
The Republican and Democrat members of the House of Representatives flew in to Tripoli on Sunday on a US navy plane, said to be the first aircraft flying the American flag to land in Libya for decades.
Mr Weldon said earlier that the delegation would also visit a university, the Libyan legislative body and "probably" a site connected to Libya's programme to develop weapons of mass destruction before leaving on Monday.
The BBC's Sebastian Usher says if nothing else, the very presence of the congressmen in what Washington has long condemned as an outlaw state represents a step forward.
In his recent State of the Union address, US President George W Bush gave Libya's announcement as an example of how his administration's foreign policy was reaping benefits.
The United Nations lifted sanctions on Libya after it agreed a compensation deal for the families of the victims of the Lockerbie bombing.
But US sanctions - which predate those of the UN - remain in place.
Just this month, Mr Bush said he had no intention of lifting them for the time being.
These sanctions are estimated to have cost Libya hundreds of millions of dollars.
But they have also cost American businesses a huge lost opportunity - with Libya's oil reserves among the highest in the world.
There is now growing pressure from US oil companies and other corporations eager to do business in Libya for the Bush administration to drop sanctions at the earliest opportunity.