The Israeli army has said it fired across the Lebanese border in retaliation after accusing Lebanese troops of gunning down one of its soldiers as he drove near the frontier.

The incident jarred the relatively stable standoff between the two neighbours, which last saw major hostilities in the 2006 war between Israel and the armed Lebanese Shia group, Hezbollah.

The Israeli soldier, Shlomi Cohen, 31, was fatally shot late on Sunday near Rosh Hanikra, by a Lebanese army sniper, the Israeli military said.

Lebanon's National News Agency reported late on Sunday that a member of the Lebanese army had opened fire at "an Israeli army unit" near the Naqoura border post but it was not clear why the sniper had opened fire.

There was no official reaction from the Lebanese army to the incident, although it issued a statement on Monday saying an Israeli drone had violated Lebanese airspace in the same area.

"At 10:15 pm (2015 GMT) yesterday, a drone belonging to the Israeli enemy violated Lebanese airspace over Naqoura, and performed a fly-over of the southern area, then left at 12:40 am," it said.

Hezbollah too did not comment on Sunday's killing.

"Whether the soldier involved in the initial shooting was a lone wolf perhaps with Hezbollah sympathies, is unknown," Al Jazeera's Nick Spicer, reporting from Jerusalem, said.

"But there are no accusations of that kind at this point. In this case, it appears to be an army on army clash," he said.

UN urges restraint

The Israeli army said the soldier was shot by Lebanese troops as he was driving a civilian vehicle along a section of the border close to the Mediterranean coast.

"After the incident, we reached the area to conduct searches as part of the investigation, and saw two suspects on the other side of the border," army spokesman Major Arye Shalicar told AFP news agency.

He said Israeli troops opened fire and hit at least one of them.

"We shot at them, and saw we hit at least one. We think they were Lebanese soldiers ... involved in the shooting of the soldier," said Shalicar.

The Israeli army immediately filed a protest with the UN peacekeeping force (UNIFIL) over what it said was an "outrageous breach of Israel's sovereignty" saying it had "heightened its state of preparedness" and would maintain its "right to exercise self-defence".

Israeli Defence Minister Moshe Yaalon said Israeli, Lebanese and UN military officers will meet on Monday to defuse tension.

In statement on Monday, Yaalon said his country regarded "the Lebanese government and the Lebanese army as responsible for what happens on their side".

"We will demand of the Lebanese army first of all an explanation as to what happened and whether this was indeed a rogue soldier; what they have done with him, and what the Lebanese army plans to do in order to prevent incidents of this kind," Yaalon said.

UNIFIL said it was urging restraint.