"The Israelis fired four rockets that fell near a Lebanese army position in the village of Adaisseh and the Lebanese army fired back," a Lebanese security official in the area said.
Lebanese news sources reported that the journalist killed was Assaf Abou Rahhal, from the Lebanese newspaper Al-Akhbar.
Lebanese witnesses said that Israeli shells are continuing to hit Adaisseh village.
The clashes erupted after Israeli soldiers reportedly attempted to uproot trees on the Lebanese side of the border.
A spokesman for Unifil, the United Nations peacekeeping force in southern Lebanon, confirmed the fighting and urged both sides to use "maximum restraint".
"Unifil peacekeepers are in the area and are trying to ascertain the circumstances of the incident and any possible casualties," said Neeraj Singh. "Our immediate priority at this time is to restore calm in the area."
The United Nations Security Council held a brief meeting about the skirmish on Tuesday afternoon. It concluded without any official statement; Alain Le Roy, the head of UN peacekeeping operations, said the UN was still investigating.
Saad Hariri, the Lebanese prime minister, called the raid a "violation of Lebanese sovereignty and demands".
He called in a statement for "the United Nations and the international community bear their responsibilities and pressure Israel to stop its aggression."
Michel Sleiman, the Lebanese president, issued his own statement denouncing the clash as a violation of UN resolution 1701. That resolution ended the 2006 war between Israel and Hezbollah, and called for both Israel and Lebanon to respect the Blue Line, the UN-administered border between the two countries.
Sleiman also called on the Lebanese army to "confront any Israeli aggression, whatever the sacrifices".
"This is a very significant development," said Rula Amin, Al Jazeera's correspondent in Beirut. "For the first time in years, clashes are taking place between Israel and the Lebanese army, not Hezbollah."
Roots of conflict
General Gadi Eisenkot, the head of Israel's northern command, predicted the clashes were a "one-time event". Eisenkot also said two Israeli soldiers were wounded in the fighting.
Avigdor Lieberman, the Israeli foreign minister, said Israel "holds the Lebanese government responsible" for the incident, and asked the Israeli envoy to the UN to file a complaint.
The fighting reportedly started when a group of Israeli army soldiers went close to the border to uproot some trees near the villages of Adaisseh and Kuferkilla.
Israeli security sources said that Israeli army engineers came under fire from Lebanese soldiers while working along the frontier and the troops shot back.
Israel said its army engineers came under fire from Lebanese soldiers and shot back [AFP]
In a statement, the Israeli military said its soldiers came under fire while they were "on routine activity in Israeli territory in an area that lies between the blue line [the internationally recognised border between Israel and Lebanon] and the security fence, thus within Israeli territory".
Jacky Rowland, Al Jazeera's correspondent in Jerusalem, said "the overall picture that seems to be emerging from Israeli television reports is that the whole incident seems to have started over some misunderstanding".
"There was some kind of Israeli incursion perceived ... to have crossed over into Lebanese territory" which precipitated the exchange of fire, Rowland said.
Israeli TV has reported that Hezbollah was not involved in the skirmish.