A Lebanese soldier has been executed by the Al-Nusra Front, the Syrian affiliate of Al-Qaeda, the government said on Saturday.

The soldier "was killed by terrorist groups who threatened to kill other hero soldiers in captivity", Defence Minister Samir Moqbel said after meeting security officials.

One of Al-Nusra's Twitter accounts announced that the group had killed the soldier it was holding hostage.

The soldier "Mohammed Hammiya, first victim of the Lebanese army's stubbornness," the Tweet read.

It was the first claim of its kind made by Al-Nusra since around 30 soldiers and policemen were kidnapped in the town of Arsal near the border with Syria, during fighting between the Lebanese army and jihadists from Syria.

The fighting in Arsal was the most serious border incident since the Syrian conflict erupted in March 2011.

In late August and early September, two Lebanese soldiers -- one Sunni and one Shiite -- were beheaded by the extremist Islamic State group, which had been holding a number of the hostages.

Hammiya was a Shiite.

In the same Tweet, Al-Nusra accused the Lebanese army of having "become a puppet in the hands of the Iranian party", a reference to the Shiite movement Hezbollah which is backed by Shiite-majority Iran and loathed by jihadists and Syrian rebels for sending forces to support Damascus in the country's civil war.

The kidnappers had been demanding the withdrawal of Hezbollah fighters from Syria and a prisoner swap for Islamist prisoners held in Lebanon.

The fighting erupted on August 2 and ended five days later with a truce, as jihadists took shelter in the mountainous areas along the Syrian border.

Since then the army has clashed sporadically with the jihadists, and on Friday two Lebanese soldiers were killed in a bomb attack on their vehicle in the Arsal area.

Lebanese forces resumed their shelling of jihadist positions in retaliation, and launched a widespread campaign of arrests.

On Saturday, soldiers stepped up artillery fire, a security source said, and the government stressed the need to "continue the confrontation" with "extremist forces".

At least 11 members of Al-Nusra and other Islamist rebel groups were killed overnight in the bombardment of the Arsal region, the Syrian Observatory for Human Rights monitoring group said.

On September 5, Al-Nusra broadcast a new video of nine Lebanese soldiers and policemen, saying that they could "pay the price" for Hezbollah's involvement in the Syrian conflict.

The war in neighbouring Syria has destabilised Lebanon, which has taken in more than one million refugees, and split the country's inhabitants between those who are sympathetic to the Syrian regime and those who back the rebels battling for its overthrow.