An Israeli military spokesman said the strike targeted "an activist linked to Islamic Jihad who was implicated in attempted terrorist actions in the Sinai."
Israeli public radio linked Ismar to last week's attacks on southern Israel's border with Egypt which killed eight Israelis.
"(He) financed the attack in the south of the country last week and was responsible for financing a major attack that terrorists were planning to carry out in the near future."
Several hours after Ismar's death, two mortar shells hit the Eshkol region, which flanks the Israel-Gaza border, Israeli police said.
Al-Quds Brigade claimed the attack and said it had fired six shells towards the Kissufim border crossing, in response to Ismar's killing.
Immediately afterwards, the air force hit "two terrorists who had fired rockets at Israel," the army said in a raid which Palestinian medics said moderately wounded two Islamic Jihad militants near Deir al-Balah.
Palestinian medics later reported finding the body of Ismael Amoum, 65, in the same area, saying it had been blown to pieces.
In a third strike, Palestinian medical sources said 20-year-old Attiyeh Moqat had been killed, and the Al-Quds Brigade claimed him as a member. Another Palestinian was wounded, said medical sources who had initially identified the dead man as Mohammed Moqat.
Israeli police said the air strike came after four rockets slammed into southern Israel without causing casualties or damages.
The Al-Quds Brigade said in a statement they fired several rockets at Israeli towns, including the large city of Beersheva in southern Israel but the army and police did not confirm the claim.
The radical Popular Front for the Liberation of Palestine (PFLP) also claimed responsibility for two rockets fired on Israel.
The exchanges raised questions over the durability of a ceasefire announced Sunday following four days of Israeli-Palestinian clashes, which killed 15 Palestinians and an Israeli.
The Hamas government accused Israel of violating the unwritten deal with its latest air strikes and called for UN intervention.
"Such aggressive behaviour confirms that Israel has no true intention of maintaining the truce and insists on escalating the situation," Hamas said.
The Egyptian-brokered truce was agreed to by Gaza's main militant groups including Hamas and Islamic Jihad. On Monday the Popular Resistance Committees also signed on.
Another rocket fired from Gaza struck Egypt and wounded a woman, the official Egyptian MENA news agency reported.
Meanwhile Prime Minister Benjamin Netanyahu convened his security cabinet on Wednesday, Israeli public radio said, two days after it had agreed to limit the response to rocket fire from Gaza.
Army chief of staff General Benny Gantz and other security officials briefed ministers on the latest events, saying they believed Hamas was trying to enforce the truce and that Islamic Jihad's fire on Wednesday morning was a response to the Israeli strike on Ismar, the radio said.
It also quoted a military source as saying Gantz ordered increased personnel and intelligence along the Israeli-Egyptian border.
Last Thursday's ambushes sparked a wave of tit-for-tat attacks in which Israeli air strikes killed 15 Gazans, 12 of them militants, the army said. Armed factions in Gaza lobbed more than 100 rockets and mortar shells across the border, killing a man.
During the hunt for Thursday's attackers, Cairo said five of its policemen were shot dead by Israeli troops and has since put pressure on the Jewish state to curb its response in Gaza.