The Nusra Front, al Qaeda's affiliate in Syria, killed one of the Lebanese soldiers it had been holding in captivity, Lebanese security sources and a Twitter statement said on Friday, Reuters reported.
The Sunni militants and other rebels in Syria regularly accuse the Lebanese army of working with Hezbollah, the Lebanese Shi'ite movement which has sent fighters to help the forces of Syrian President Bashar al-Assad.
Two Lebanese soldiers were also killed by a roadside bomb on Friday near the border town of Arsal, security sources said, the first such attack since Islamist militants from Syria staged an incursion there last month in the worst spillover to date of the Syrian civil war into Lebanon.
Islamist gunmen including fighters affiliated with the Islamic State group seized a number of Lebanese soldiers during that incursion. Islamic State militants have beheaded two of those soldiers since then.
Friday's killing was the first reported to have been carried out by the Nusra Front, which along with Islamic State is holding over a dozen more Lebanese soldiers captive.
The Twitter statement on an account affiliated with Nusra Front, said the soldier had become "the first victim of the intransigence of the Lebanese army which has become a plaything in the hands of the Iranian party", referring to Hezbollah.
The Sunni militants have been demanding the release of Islamists held in a Lebanese jail.
Three soldiers were wounded by Friday's bomb, which hit a military personnel carrier.
Following the bombing, soldiers raided houses in the town in search of militants, security sources said, and later, according to the state news agency, the army used "heavy weapons" to target militant positions around Arsal.
The Sunni Muslim town, has become a refuge for tens of thousands of Syrians fleeing the country's civil war.
Two rockets fell in the area of the town of al-Labwe near Arsal but no casualties were reported, security sources said.
Earlier on Friday, Lebanese soldiers arrested two Syrians in the Bekaa Valley town of Baalbek who had confessed to belonging to the Nusra Front, security sources said.
Security forces also detained six Syrians in the predominantly Shi'ite town of Nabatiyeh in southern Lebanon who had confessed to membership of "terrorist groups", a security official said. One had been found in possession of explosive belts, he said.