A 65-year-old Palestinian man and three children were injured early Thursday in an Israeli airstrike, said Gaza Strip Health Ministry spokesman Ashraf al-Qedra.
The four were taken to hospital with light to moderate shrapnel injuries, he said.
Israel launched strikes at five targets in southern Gaza late Wednesday and then four more targets in northern Gaza early Thursday, in response to mortar attacks on Israeli troops along the border.
The Israeli military said that during searches for tunnels dug by militants to carry out attacks it had found a tunnel running underneath the southern Gaza border at a depth of about 27-29 metres.
It was not yet clear how long it was, but the military said it probably reached far into Israel.
A military spokesman said its troops had come under fire from mortar shells while searching for tunnels in the Gaza Strip.
Until now, Hamas, the Islamist movement in de facto control of the Gaza Strip, had "tolerated" Israeli troops entering 100 metres into the Gaza Strip to search for tunnels, the spokesman said.
One target struck by Israel early Thursday was a goldsmith workshop in southern Gaza City, residents said. Israel says it has intelligence on which workshops are used to produce weapons. The civilians injured in the bombing lived nearby.
An Israeli military statement said the targets were part of the "infrastructure" belonging to Hamas' armed wing.
Israel and Hamas accused each other of escalating tensions over the volatile territory.
Sources close to Hamas, who spoke on condition of anonymity, said that Egypt had intervened between Hamas and Israel to defuse the growing tension.
Musa Abu Marzooq, a top Hamas leader based in Qatar, wrote on his Facebook page in Arabic that the two sides had accepted an Egyptian call to return to a fragile ceasefire that has largely remained in place since the 2014 Gaza war.
Meanwhile, Palestinian leaders in the West Bank announced late Wednesday that they would "immediately" implement a March 2015 decision to suspend security cooperation with Israel.
The Palestinians' West Bank leadership has long threatened to suspend such cooperation - seen as essential by the international community to maintain relative calm in the West Bank - but now says it will no longer tolerate Israeli military raids into Palestinian cities.
Israel insists that such arrest raids are also essential to foil attacks constantly being planned by radicals.