At least five people were injured in the first attack
Separate Israeli air attacks have killed at least four Palestinian militants, including an Islamic Jihad commander, in the Gaza Strip.
Two militants were killed and another died later after they had reportedly fired a rocket-propelled grenade at Israeli soldiers across the border.
Overnight, Israel killed Islamic Jihad commander Khalid Shaalan, accusing him of a role in rocket attacks.
Violence has flared sporadically since the truces called over Gaza in January.
The Israeli military said its aircraft had attacked three armed men on Thursday after they fired at soldiers over the border.
Islamic Jihad said the men had been returning together to their homes in central Gaza after a night spent on patrol along the border, the Associated Press reports.
Two died instantly and the third man died later in hospital from his wounds, witnesses said. A fourth militant was also injured.
Following the air strike, four rockets were fired from Gaza into Israel causing no injuries, the Israeli military said.
Pattern of violence
Khalid Shaalan was killed and his deputy commander was seriously injured in a missile attack on Wednesday evening in the north of the strip, Palestinian and Israeli sources report.
At least four people were also injured when a missile hit the two men's vehicle in the town of Beit Lahiya.
An Israeli army spokesman said Mr Shaalan had been "targeted and killed" for his involvement in recent rocket attacks on the Israeli city of Ashkelon.
An Islamic Jihad spokesman vowed to "avenge this aggression", AFP news agency reports.
Less than two months since Israel's massive military offensive in Gaza - in which some 1,300 Palestinians died - violence in the region has settled into a familiar pattern, the BBC's Aleem Maqbool in Gaza City reports.
Missiles are regularly fired by Palestinian militants, albeit mainly into open areas, and the Israeli air force responds with air strikes.
With stalled talks between Hamas and Israel on a long-term ceasefire agreement, people in Gaza and Israel's border towns are unsure how the pattern will be broken, our correspondent adds.