Israel has continued to target tunnels in the smuggling hotspot of Rafah
Israeli jets have bombed tunnels on Gaza's border with Egypt, after two rockets were fired at southern Israel.
The Israeli military said the air attack targeted a tunnel used for smuggling arms into Gaza.
A little-known militant group called Hezbollah Brigades Palestine claimed responsibility for the rocket attacks, which caused no casualties.
The violence came amid moves to turn ceasefires that ended Israel's 22-day offensive in Gaza into a lasting truce.
Two rockets fired from Gaza landed in Israel on Monday morning, the Israeli military said.
Several hours later, Israeli jets bombed a border area in the southern Gaza town of Rafah.
Palestinian officials said a 25-year-old Gaza man was killed and five people were injured in an explosion in northern Gaza near the border with Israel.
The explosion was apparently caused when an unexploded munition was thrown into a fire being used to melt down scrap metal.
Sporadic violence has continued between Israel and Gaza since Israel ended its offensive on 18 January and the Hamas movement declared a ceasefire.
Egypt has been trying to mediate a long-term truce. About 1,300 Palestinians and 13 Israelis were killed in the 22 days of violence.
Hamas wants Israel to open Gaza's blockaded border crossings, but Israel said on Saturday that it would only do so if Hamas released an Israeli soldier it helped capture in 2006.
Hamas wants Israel to release hundreds of top-level Palestinian militant prisoners in return for Cpl Gilad Shalit's freedom.
Separately, a leading Israeli newspaper says the Israeli civil administration in the West Bank has designated an area of 172 hectares (425 acres) as state land.
Haaretz says the decision could pave the way for some 2,500 new settlement homes to be built.
However, several steps of government approval are required for building work to begin, which the newspaper says means construction is still a long way off.
Israeli has pledged to freeze settlement activity on occupied land, but it has continued to expand existing settlements, built in defiance of international law since 1967.
Right-wing parties which fared well in Israeli elections on 10 February are strong supporters of the settlement movement, which is seen as a major obstacle to the two-state solution supported by the US.
The settlement of Efrat, south of Jerusalem, is at the centre of the latest expansion plans. The mayor says he wants the 1,600-family settlement to grow to 30,000 residents.
More than 400,000 Israeli settlers live in the West Bank and East Jerusalem, which Israel captured in the 1967 war.