Libya has said families of victims of the Lockerbie disaster may not be fully compensated unless the United States ends sanctions by 12 May, 2004.
Mr Ghanim said Libya should be paid for scrapping its weapons
Prime Minister Shukri Ghanim told the New York Times the US must honour an agreement signed last September to lift the penalties within eight months.
Mr Ghanim also said Libya should be rewarded for abandoning its banned weapons programme.
A US envoy was due in the UK for talks on how to verify Libya's disarmament.
Mr Ghanim told the newspaper: "The agreement says that eight months after the signing, if American sanctions are not removed, then the additional £6 million for each family of victims will not be paid.
"We will leave this to the decision of the Americans," he added.
Libya has so far paid $4m each to the families of the 270 people killed when a Pan Am Flight 103 exploded over Lockerbie in Scotland in 1988.
A bomb planted by Libyan agents blew up on board the aircraft.
The newspaper quoted a US State Department spokesman as saying he could not comment on Mr Ghanim's comments.
Lifting US sanctions would unfreeze about $1bn in assets Libyan officials say are held in US banks, as well as allow US oil companies to return to Libya.
US 'should act quickly'
The Libyan prime minister said Libya should be paid for handing over nuclear-related materials as it dismantles its nuclear weapons programme.
Libya announced its decision to scrap its weapons of mass destruction programme last month.
Mr Ghanim said his country wanted to "accelerate to the maximum" ending the project.
He told the New York Times America should act quickly to reward Libya's actions.
The US under secretary of state for arms control and international security, John Bolton, was due in London on Friday for meetings with British officials about how to verify Libya is scrapping its weapons.