The Syrian army and Lebanon's Hizballah militant group, which are waging a separate campaign on the other side of the border, also announced a cease-fire.
He said the remains would be subject to DNA testing to ensure their identities but that he was "almost certain that the case is closed".
Hezbollah's Al Manar TV reported that the armed group has received the bodies of five of its fighters who were held by ISIL. The surrender of the remains of the fighters by the extremists took place at the border crossing of Mira. Hezbollah is fighting alongside Syrian regime troops.
News of a pause in fighting on the Lebanese side of the border came as Hizbollah announced a ceasefire with ISIL on the Syrian side, in the western Qalamoun region.
The two sides say they have driven the militants from most of the border region.
The Lebanese army said it is not coordinating its military operations with the Syrian army.
Abbas Ibrahim, the chief of Lebanese General Security, said six bodies buried in Lebanon near the border with Syria were removed. The sit-ins have been held since the soldiers were captured by ISIS in 2014.
Straight As for 96 Altrincham Grammar School for Girls students
Notably, a significant 92 pupils achieved all A* and A grades, with 33 individual pupils securing 10 or more A* grades. The Art department saw 100 per cent A* to C results with one pupil not dropping a single mark for their A* grade.
Some reports suggested that the IS militants had already killed the Lebanese soldiers, as reports said Hezbollah was told by IS about their destiny, but the Shiite group will leave the declaration about the fate of the soldiers to the Lebanese army. Damascus and the Lebanese militia movement Hezbollah are also now carrying out their anti-Daesh offensive on the Syrian side of the border.
Hezbollah sources in Lebanon said the Islamic State had "succumbed under fire and asked for negotiations".
The 9 Lebanese soldiers have been missing since August 2014, when ISIS and then Al-Qaeda affiliate Al-Nusra Front briefly overran Arsal, a town on Lebanon's restive eastern border with Syria.
Coordinating with Hezbollah would be politically sensitive as Lebanon is a U.S. ally, and the USA has designated Hezbollah a terrorist organization.
Last week, Lebanon and Hezbollah each announced they had made significant gains against ISIL fighters, driving them back into a smaller part of the arid hills on the border.
"We see no evidence of substantive cooperation (between the army and Hezbollah)", the diplomat added.