Four Palestinian family members, including two children, have died in Gaza, in an Israeli artillery strike.
Another 12 people were wounded when an Israeli tank shell hit a home on the eastern outskirts of Gaza City.
Israeli Defence Minister Ehud Barak said it was an unfortunate mistake, but added that was "the price of dealing every day with the terrorists".
In a second attack, three people - all members of Islamic Jihad - were killed during an air strike, medics said.
On Saturday, Palestinian militants fired a barrage of rockets over the frontier, prompting Israeli retaliation.
The BBC's Jon Donnison, in Gaza City, says the exchanges are among the most serious since Israel's major offensive in the coastal strip between December 2008 and January 2009.
Our correspondent adds that, unusually, the militant wing of Hamas claimed responsibility for at least a dozen of the mortars fired at Israel over the weekend.
In Tuesday's first attack, a grandfather and two of his grandchildren were among those killed when artillery was fired at a house, reports said.
Witnesses said they were playing football when they died.
The Israeli defence minister said: "We were not glad of it but that's the price of dealing every day with the terrorists attacking our civilian population from within civilian population on the other side."
Palestinian emergency services said the second attack struck the Zeitun quarter of eastern Gaza City, AFP news agency reports.
Doctors from the health ministry in Gaza say those who died are believed to have been militants from the Islamic Jihad group.
The latest deaths came a day after Palestinian doctors said at least 17 people were injured in Israeli air strikes in Gaza.