Later in the day, further rockets or mortar rounds from Gaza were intercepted, the army said. No Palestinian casualties were reported.
"All factions, including Hamas and Jihad, are committed to understandings for calm", Jihad spokesman Dawoud Shihab told AFP.
The Israeli military released video which they say shows strikes against military targets in the Gaza Strip.
Egypt was said to have performed a significant role in stopping violence in Gaza from sliding into full-blown military conflagration during the last escalation on the border.
The protests peaked May 14, the same day the USA opened its embassy in Israel's capital, Jerusalem, when more than 60 people died in a Hamas-organized action to breach the Israeli border and return to homes that were lost 70 years ago during the war that established Israel. Hamas sources said: "Our military wing has picked up the struggle and we want to let our leaders know that all options are on the table".
Among the targets were rocket launchers designed for terrorism, a lathe for the manufacture of rockets and rocket engines, advanced naval weapons, military compounds, training camps and sites for the manufacture of weapons.
This includes Israeli settlement policies in the occupied West Bank and East Jerusalem, as well as the recent round of bloodshed in the Gaza, where Israeli fire killed over 100 Palestinians during mass protests along the Gaza border, Malki added.
Palestinian militants continued to fire additional barrages toward southern Israel, setting off air raid sirens in the area throughout the night.More news: As Starbucks closes, Chicago black-owned coffee shop opens up racial discourse
The Israeli military said most of the projectiles fired Tuesday were intercepted, but three soldiers were wounded.
Prime Minister Benjamin Netanyahu said that the country's army would "respond to these attacks powerfully".
Islamic Jihad announced an Egyptian-brokered ceasefire agreement with Israel.
The armed wings of Hamas and Islamic Jihad claimed responsibility for the firing, saying it was in response to Israel's killing of dozens of Palestinians since March 30, majority in Gaza border protests.
Israel and Hamas are bitter enemies and have fought three wars since the Islamic group seized control of Gaza in 2007.
Security Council statements are adopted by consensus by all 15 members. No Israelis have been killed.
At least 121 Palestinians have been killed by Israeli fire in the unrest.
Amid global condemnation of its use of lethal force at the mass demonstrations that began on March 30, Israel said numerous dead were militants and that the army was repelling attacks on the border fence.
Kuwait first put forward the idea 10 days ago after condemning Israeli forces' killing of dozens of Palestinians during protests on the Gaza border.