United Nations peacekeepers in the region have managed in the past few hours to negotiate a cease-fire despite sporadic gunfire, officials said.
Local reports said the two dead were a fighter from Lebanon's Hezbollah group and a Palestinian fighter.
The clashes began at dawn on Sunday, after Palestinian fighters fired rockets at northern Israel and Israeli aeroplanes responded with air strikes on Palestinian bases near the Lebanese capital, Beirut.
Witnesses saw black smoke rising from a military base outside Beirut and another in the eastern Bekaa Valley, both run by the Popular Front for the Liberation of Palestine-General Command (PFLP-GC) which is based in Damascus.
Later, Hezbollah fighters opened fire on Israeli soldiers along the border and fired more rockets into Israel, with Israeli forces returning fire, the army said.
One Israeli soldier was wounded in the rocket attacks, the Israeli army added, while Israeli civilians living in towns along the border were also ordered into bomb shelters.
Ehud Olmert, the Israeli prime minister, warned of a "clear and harsh response" if the attacks did not stop.
Islamic Jihad has since claimed responsibility for the rocket attacks in a statement.
The barrage is the first to have been fired into Israel since February 3, an Israeli military spokeswoman said.
It came two days after a senior Islamic Jihad official and his brother were killed in a car bombing in southern Lebanon that the Palestinian group blamed on Israel.
Lebanon's Hezbollah group, which controls the Lebanese side of the border, also blamed Israel for the assassination and Islamic Jihad officials swore revenge.