The deadline for a compensation deal between Libya and the families of those killed in the 1989 French airliner bombing passed on Saturday without agreement.
The UTA bombing claimed 170 lives
Hours before the ultimatum, Libya invited a delegation of relatives to continue talks in Tripoli on Monday - a move welcomed as a "positive sign" by the families' spokesman.
Earlier, French President Jacques Chirac warned Libya that ties with France would suffer if it failed to stick to its commitment to offer an increased settlement.
Last month France lifted a threat to block a United Nations resolution ending sanctions against Libya over the 1988 Lockerbie airliner bombing unless a similar compensation deal was agreed for the 170 who died in the Niger attack.
France had protested that an earlier settlement was dwarfed by the $2.7bn Libya agreed to pay in connection with the Lockerbie bombings.
Under a preliminary agreement, Libya and negotiators for the French families were meant to have reached a definitive deal by Saturday.
"I don't want to imagine that these promises won't be adhered to," said President Chirac before the deadline.
"But if, by chance, they were not met, this would no doubt have consequences on the relations between our two countries."
He added: "I say this without aggression, but without weakness."
A spokesman for the families, Guillaume Denoix de Saint Marc, remained confident that a solution would be found - and said he believed Libya's failure to meet the deadline was due to organisational problems on its part and not a change of heart.
He described the invitation to continue talks in Tripoli as "a positive sign of the will to move forward".
However, others are less convinced.
First imposed in 1992
Bans on flights, arms sales, and oil exports
Freeze on Libyan funds
Reduce Libyan diplomatic representation
Suspended, but not lifted, in 1999
Francoise Rudetzki, one of those involved in the talks, told Associated Press she hoped President Chirac's comments would prompt Libya into action. "We're still waiting for a sign from Libya," she said.
Abderaman Koulamallah, whose sister and five of her children died in the bombing, said: "France should take severe diplomatic measures."
All those on board the DC-10 UTA airliner died when it exploded in the skies over the West African state of Niger in September 1989.
Tripoli has never accepted responsibility for the bombing - despite the conviction of six Libyan officials tried in absentia by a French court in 1999.
Libya refused to extradite the six, who include Colonel Gaddafi's brother-in-law, and has always maintained their innocence.
However, it agreed to pay out $33m demanded by the court in compensation.
After the $2.7bn Lockerbie deal was announced in August, France demanded a more "equitable" settlement for families of those killed in the UTA bombing.