YARZE, Lebanon: The Lebanese Army Tuesday pounded Daesh (ISIS) from land and air, pushing the militants into a diminishing corner of territory during the third phase of “Fajr al-Joroud.”

“The Army took over one of the most difficult areas and one of the highest peaks in its operations today,” Army spokesman Brig. Gen. Ali Qanso said during a media conference Tuesday afternoon at the Defense Ministry in Yarze.

The Army, Qanso added, took over 20 square kilometers including a key strategic hilltop in the northeastern outskirts of Al-Qaa from Daesh, “bringing the total landmass recaptured to 100 square kilometers out of 120 square kilometers.”

The spokesman also said that only 20 square kilometers remained under Daesh control.

However, the advances made by the Army Tuesday came at a cost, as one soldier was killed and four were wounded while dismantling an explosive device on the outskirts of the northeastern town of Arsal. The soldiers were from an Explosive Ordinance Disposal unit, a military statement said.

The Army took over nine Daesh posts and captured a number of arms caches. Hideouts, caves and a communications room used by Daesh were also taken.

The Army said it killed around 10 militants during the clashes, in a post on its official Twitter account at around 6 p.m.

Qanso told reporters that the exact number of militants killed since the start of the operation was not available for public release. During the first two days of the operation, which began Saturday, the Army announced that 35 Daesh militants were killed. Ahead of the offensive, officials estimated that between 550 and 600 militants were entrenched in the outskirts of Ras Baalbeck and al-Qaa. Qanso also said that no new information was available on the status of the nine Lebanese soldiers who were kidnapped by Daesh after they briefly overran the town of Arsal in 2014. “But we have not, for one day, forgotten about the kidnapped soldiers and this is our primary concern. Once we finish this battle, and if no information is revealed, the Army will act accordingly,” Qanso said.

The spokesman added that the Army was abiding by international standards of armed conflict in its conduct.

When asked about potential cooperation with Hezbollah as the Army pressured militants toward Syrian soil, Qanso said: “From day one we said we would fight for the last [inch] of Lebanese territory, push them out and then stop there.” The military had repeatedly denied any coordination with Hezbollah and the Syrian army who are waging their own campaign against Daesh inside Syria.

The Army recorded a video shown at the conference depicting the rugged terrain and steep valleys making it a difficult battle for the attackers.

“The engineering unit is continuing to clear the land of explosive devices and paving the roads for the Army to make its way to face militants still seeking refuge in the hilltops,” Qanso said.

Meanwhile, Defense Minister Yaacoub Sarraf praised the Army as he spoke from a military expo in Moscow. “I am here to find ways to strengthen our Army and request military aid.”

“We will, without a doubt, look to exchange information [with attendees at the conference] of the kidnapped soldiers, the [missing] bishops ... and [missing] Sky News Arabia reporter Samir Kassab,” he added.

Sarraf said agreements were reached with Romania to refurbish Lebanese tanks, as well as acquiring equipment from Armenia, Brazil and Canada to strengthen the Army in its capability to fight terrorism.

Around noon, the military announced that it had seized the strategically important Ras al-Kaf hilltop near Al-Qaa – a significant gain given the elevated position and excellent line of fire on territory still controlled by militants. The military added that its units had been examining the surrounding area, combing the land for landmines and weapons.

The capture of Ras al-Kaf is expected to give the Army an upper hand in the fight against Daesh, tightening the noose on Daesh militants.

The development came after the military announced that it had initiated the third phase of its Fajr al-Joroud offensive against the militants to secure all remaining territory from the group.

The soldier killed was identified as Lance Cpl. Abbas Kamal Jaafar, born March 19, 1983, from Tyre, according to the military statement.

Jaafar, who was married, had received commendations on several occasions from the Army Command and the interior minister, the statement added.

A ceremony honoring the slain soldier will be held 8 a.m. Wednesday at the Central Military Hospital in Badaro, before funeral prayers, are held at 3 p.m. in in his hometown of Tyre, where he will be laid to rest.

The state-run National News Agency reported that two of the soldiers wounded Tuesday were transferred to a hospital in Beirut via military helicopter, while the others were transferred by the Lebanese Red Cross to nearby hospitals.

The loss of Jaffar brings the Lebanese Army’s death toll in the offensive to four since the battle began Saturday. Around 17 have been wounded so far.

In a joint statement, the International Support Group for Lebanon expressed its backing for the Lebanese Army’s offensive, praising the Army’s efforts to “shield Lebanon’s territorial integrity and security” and offered condolences for the slain soldiers.

“The members of the ISG reiterate their strong and unanimous support to the [Lebanese Army] as the defender of Lebanon,” the statement said. “The members of the ISG call for continued international support to further strengthen the [Army’s] capabilities.”

President Michel Aoun praised the Army’s offensive in comments published Tuesday in local daily Al-Liwaa. Aoun noted that eliminating the militants’ presence would bolster Lebanon’s security.

Aoun added that the security situation in Lebanon was good – better even than the situation in some European countries. This was due to the efforts of security agencies to dismantle extremist cells, he said, and to cooperation between various government agencies.