London's ambassador to France, Sir John Holmes, said on Wednesday that the vote will be put back to next week.
Britain drafted a UN Security Council resolution to end sanctions against Libya after Tripoli agreed to pay $2.7 billion to the families of those killed in the 1988 Lockerbie bombing.
But France, a veto-wielding Security Council member, vowed to block the move unless Libya increases the $34 million it has paid to victims of the 1989 bombing of a French UTA airliner.
Libya has not admitted responsibility for the UTA bombing, which killed 170 people.
But it paid out compensation after a Paris court convicted six Libyans for the bombing in absentia.
A Libyan was convicted in a Dutch
court for the Lockerbie bombing
Holmes said London supported the French families' attempts to secure a larger award but said there were limits to how long it would wait for a settlement.
"We cannot wait indefinitely. We want to ratify the agreement we have with the Libyans," he said.
Britain has not set a deadline for a deal, said Holmes, "but of course, we are talking of a few days, a few weeks, but not a lot of time."
Sources say the UTA bombing relatives want compensation equivalent to the $120 million secured by relatives of those who died in the Concorde crash near Paris in 2000.