The Syrian government has held on to a pocket of territory in the provincial capital of Deir al-Zor city, and at a nearby air base.
The group's War Media channel said the unilateral pause was "in the framework of a comprehensive agreement to end the battle in west Qalamun against Daesh (IS)".
Both offensives have advanced toward the border from opposite sides. Hezbollah's TV said the group is also expected to remove bodies of five of its own fighters killed in the area.
Eight Lebanese soldiers who have been in Islamic State captivity since 2014 are nearly certainly dead, the head of Lebanon's internal security agency said on Sunday.
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The Lebanese army has said it is not coordinating its attack with Hezbollah or the Syrian army.
The truce was declared to pave the way for final negotiations linked to the fate of soldiers abducted by the terrorists in 2014.
The troops were among 30 soldiers and police kidnapped by ISIL and al-Qaeda's former Syrian affiliate when they overran the Lebanese border town of Arsal in August 2014.
Nine troops remained missing, but today Ibrahim spoke only of eight bodies and said he was "almost certain that the case is closed".
The Lebanese army had previously said there would be no negotiations with ISIL, though Hizbollah leader Hassan Nasrallah suggested in a speech last week that his group might engage in talks with the extremists.
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Others called for Zinke to publicize details of the report, which is under review at the White House. There are concerns that changes to the designation could affect the local economy.
Nusra militants and a Syrian rebel group withdrew from Lebanon's border region earlier this month.
Hizbollah has provided critical military support to Syrian President Bashar Assad during Syria's six-year-long war. Along with elements of the Syrian army and Hezbollah, the Lebanese are trying to evict ISIL from positions within Lebanon, and have been gaining ground, but the pause has been called to allow for a period of negotiations.
Hezbollah and its allies have been pressing the Lebanese state to normalise relations with Damascus, testing Lebanon's official policy of neutrality towards the conflict next door.
"We see no evidence of substantive cooperation (between the army and Hezbollah)", the diplomat added.
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