Defence Minister Moshe Yaalon warned on Wednesday that Israel would respond to any attacks on its territory and not allow its people to come under fire "in any form".
His warning was issued after militants in Gaza fired a rocket at southern Israel, and as a Syrian mortar round and small arms fire hit the Israeli-occupied sector of the Golan Heights.
The Israeli military was quick to respond in both cases, with a tank firing back across the Syrian armistice line towards the source of fire and the air force mounting three air strikes on Gaza, in the first such raids in more than four months.
"We shall not allow in any form the establishment of a routine of sporadic firing at our civilians or our forces," Yaalon said in a statement communicated from his office.
Prime Minister Benjamin Netanyahu also issued a stern warning.
"If calm is disrupted, we will respond forcefully. The security of the citizens of Israel is my top priority and we know how to defend" them, he said on meeting Norway's Foreign Minister Espen Barthe Eide in Jerusalem.
Yaalon said Gaza's Hamas rulers were responsible for any fire directed at Israel from the coastal enclave, and in the same way, President Bashar al-Assad's regime was to blame for whatever fire emanated from Syria.
After the overnight Israeli strikes which hit open fields near Gaza City and in the north, causing no damage or injuries, militants fired two more rockets at Israel, police said.
Both landed in an open area near the border town of Sderot, causing no casualties.
The rocket fire on both days was claimed by radical Salafist Islamist group the Mujahedeen Shura Council, which said it was a response to the death of a Palestinian prisoner who died of cancer while serving life in an Israeli jail.
"In response... to Jewish crimes against oppressed prisoners, we struck Sderot which squats on Muslim lands north of Gaza using six missiles on the morning of April 3," a statement said.
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The Gaza border has been largely quiet since November when an Egypt-brokered ceasefire ended a deadly eight-day confrontation between Israel and Hamas militants.
Until five weeks ago, the truce deal had been completely respected by both sides.
But since late February, there have been four instances of rocket fire on Israel, three of which were claimed by Salafist militants.
The rocket fire from Gaza prompted a statement of concern from UN Special Coordinator for the Middle East peace process, Robert Serry.
"It is of paramount importance to refrain from violence in this tense atmosphere and for parties to work constructively in addressing the underlying issues," he said in remarks released by his office.
Violations of the ceasefire risked "unravelling the gradual but tangible improvements achieved since (the truce deal)," he said.
On the Golan Heights, there has in recent months been an uptick in stray fire from the two-year civil war raging in Syria, with Israeli forces firing back at the source of the shooting.
"A mortar shell from Syria landed... in the southern Golan Heights," an army spokeswoman told AFP late on Tuesday, saying troops "returned precise fire at the source and reported a direct hit."
Last week, troops fired an anti-tank missile at a Syrian army post after coming under fire twice in 12 hours.
Israel is closely monitoring the ceasefire line with Syria out of concern that jihadist elements among the rebels fighting the Assad regime could attack the Jewish state.
Israel seized the Golan from Syria in the 1967 Six-Day War and annexed it in 1981, in a move never recognised by the international community.