Islamic State has held nine Lebanese soldiers captive since 2014, when it briefly overran the border town of Arsal in northeast Lebanon with other militants - one of the worst spillovers of Syria's war.
"The army command announces a ceasefire beginning at 7:00 am (0400 GMT) to make way for the last phase of negotiations linked to the fate of the kidnapped soldiers", it said in a statement on Sunday.
Coinciding with the military operation, Lebanese group Hezbollah also announced that its fighters, along with Syrian regime forces, had begun an onslaught to recapture the outskirts of Qalamoun from Daesh in western Syria.
Hezbollah, however, said that fighters from the Islamic State, also known as ISIS or ISIL, had surrendered, had turned over the bodies of two Hezbollah combatants and had agreed to help determine what had happened to a number of missing Lebanese army troops.
Both offensives have advanced towards the border from opposite sides.
Al-Nusra admitted defeat after six days of fierce fighting and handed over five Hezbollah fighters in return for evacuation of its members to a region in neighboring Syria.
Families of the missing soldiers and dozens of media outlets waited near the parliament in Beirut on Sunday after Lebanese General Security chief Abbas Ibrahim announced that the issue would be resolved by the end of the day.
The Lebanese army offensive against ISIL has been working to drive the group out of its last border footholds in the areas of Jurud Ras Baalbek and Jurud Al Qaa.
The Lebanese army has said it is not coordinating its attack with the Syrian army or Hezbollah, which Washington classifies as a terrorist group.
In exchange for locating the bodies of the soldiers kidnapped in 2014, the militants will be evacuated to eastern Syria.
Any coordination between the Lebanese army and either the Syrian army or Hezbollah would be politically sensitive in Lebanon and could jeopardise the sizeable United States military aid the country receives. However, reports from the field indicate that Hezbollah has been directing the operation from the Lebanese side and has not been acting under the direction of the Lebanese army.