The exchange occurred one day after Saad Harriri announced that he was stepping down as Lebanese prime minister-designate. The opposition had rejected his cabinet proposals.
Some analysts had worried that the absence of a government in Lebanon could lead to a power vacuum and a deteriorating security situation.
Israel fought a month-long war in 2006 against Hezbollah, a group originally set up to fight Israeli occupation of southern Lebanon and which maintains strong support among Lebanon's Shia Muslims.
Hezbollah has not claimed responsibility for firing Friday's rockets.
Palestinian factions in southern Lebanon have previously been suspected of firing rockets into Israel.
Zeina Khodr, Al Jazeera's correspondent in the Lebanese capital, Beirut, said that rockets had been fired into Israel since the 2006 war.
"In most occasions there have been no claims of responsibility or officials in Lebanon have blamed extremist groups - sometimes Palestinians, sometimes groups linked to al-Qaeda.
"The timing is important. First of all, the Israeli army carried out a major military exercise along the border this week.
"They said that they were preparing for a possible war - an exercise that simulated intense warfare.
"It also comes weeks after Binyamin Netanyahu, the Israeli prime minister, told Hezbollah that they will be held responsible for any action that they take if Hezbollah officials are part of the new government in Lebanon.
"Hassan Nasrallah, the secretary-general of Hezbollah, interpreted that statement saying that he didn't expect that a war would happen in the near future but efforts by Israel to block the formation of a new government."
Lebanon has been without a government for more than two months.