The UN-backed Libyan government accused rivals of breaking a ceasefire minutes after it was supposed to take effect, stating if it happened again they would respond violently.
The agreement between Libya's warring eastern and western administrations, if it holds, would mark the first break in fighting in months.
A spokesman for the Libyan Arab Armed Forces, who fight for the eastern authorities, said that the ceasefire took effect early on Sunday, warning that any violations of the ceasefire from the opposing side would be dealt with "severely".
But the UN-backed prime minister of the western government, Fayez Sarraj, conditioned the armistice on rival forces withdrawing from the outskirts of Tripoli - indicating hostilities could continue if this does not happen. It is not yet clear if Khalifa Haftar, head of the Libyan Arab Armed Forces, will agree to remove his forces from the capital.
Since Haftar's forces launched an offensive in Tripoli in April there have been international efforts to try to contain the crisis.
Libya is governed by duelling authorities, one based in the east which is backed by Haftar and one in Tripoli in the west, led by Sarraj.
The eastern administration is supported by the United Arab Emirates, Egypt, France and Russia while the western government is backed by Turkey, Qatar and Italy.
Earlier this week, Turkish President Recep Tayyip Erdogan and Russia's leader Vladimir Putin released a joint statement calling for a January 12th truce.
This came after Europe launched a diplomatic campaign to try to prevent Libya from becoming a second Syria. Along with the UN, European powers have called for a peace summit to happen in Berlin early this year to bring together the leaders of the rival governments.
Russia and Turkey have been accused of inflaming the conflict by giving military aid to its respective parties.