AMMAN (Reuters) - Three Lebanese soldiers were killed and one was critically wounded on Sunday when their armored vehicle hit a landmine on the Lebanese-Syrian border, a security source said.

The area where the soldiers were killed was near a border stronghold close to the mountains of Arsal, where Shi’ite Hezbollah militia recently forced Sunni Syrian militants to leave in a joint cross-border operation with the Syrian army, the source added.

The Lebanese army had launched an offensive on Saturday against an Islamic State enclave on the northeastern border with Syria.

The Lebanese Shi’ite group Hezbollah also announced an assault on the militants from the Syrian side of the frontier.

An army spokesman said on Sunday that more than two thirds of the area that was in the hands of the militants had been recaptured since the offensive began.

“We are committed until the destruction of Daesh on Lebanese soil,” he said, using a pejorative term for Islamic State and adding that some militants had handed themselves over to the army, though he did not give numbers.

Two suicide bombers, one on a motorcycle and the other driving a motor vehicle, were foiled in an attempt to target soldiers, the spokesman said, adding that 15 militants were killed in direct combat, shelling or aerial strikes on Sunday.

On Saturday the army said that 20 militants were killed and 10 soldiers were injured.

The Lebanese army spokesman said that it was not coordinating the assault with Hezbollah or the Syrian army.

Any joint operation between the Lebanese army on the one hand and Hezbollah and the Syrian army on the other would be politically sensitive in Lebanon and could jeopardize the sizeable U.S. military aid the country receives.

Many rebels, alongside thousands of Sunni refugees who fled after the Syrian army and Hezbollah regained control of towns and villages they had overran in the early years of the conflict, took shelter on the Lebanese side of the border strip.

Northeastern Lebanon was the scene of one of the worst spillovers of Syria’s war into Lebanon in 2014, when Islamic State and Nusra Front militants attacked the town of Arsal.