Direct confrontations between Israel and Gaza's governing Islamists have been rare since their 2008-2009 war, though fighting with smaller Palestinian factions has persisted. A flare-up last month killed nine Gazans, including Hamas members, and prompted neighbouring Egypt to broker a ceasefire.
In Gaza City, an Israeli air strike killed a Hamas gunman and wounded a comrade, the faction said. The Israeli military said the man targeted had been preparing to fire a short-range rocket into Israel.
Separately, Israeli troops shelled a vehicle in the eastern Gaza Strip, wounding three Palestinians who medics identified as fighters. The army said the Palestinians were trying to launch an anti-tank missile at one of its border patrols.
On Monday, heavy machine-gun fire from Gaza struck cars some 3 km (2 miles) inside Israel, causing no casualties, the military said. No Palestinian faction claimed responsibility.
"The Hamas terror organisation is solely responsible for any terrorist activity emanating from the Gaza Strip," the Israeli military spokesman said in a statement on Thursday.
But a senior Israeli politician struck a different note, telling a Tel Aviv think-tank that Hamas had been making a "big effort" to prevent cross-border shelling by other Gaza factions.
"All this is not a result of love of Zion, but because of Israeli deterrence," Deputy Prime Minister Dan Meridor told the Institute for National Security Studies. "They do not want to be dragged into another round (of fighting) which for them - mainly for them - would be very tough."