Hamas and Israeli forces worst clashes erupt in Gaza
Since the confrontations broke out, Hamas and other militant groups have fired bullets and mortar rounds on at least 10 occasions, and the Israeli air force has carried out at least three bombing raids.
Israeli tanks stationed on the border have also fired multiple times at what the army said were Hamas targets.
Late on Thursday afternoon, tank shelling that followed a mortar attack from the Khan Yunis area in southern Gaza killed Zeina Al-Amour, 54, according to the Nasser hospital that pronounced her death.
A 21-year-old was also wounded in artillery shelling in the area.
The shelling came after a night in which air raids wounded four people, three of them children, medical and security officials said.
The Palestinian attacks were targeting Israeli forces working near the border fence searching for tunnels crossing under the border, like those whose destruction it cited as one of the main achievements of the 2014 conflict.
The army announced a new tunnel was found on Thursday, after a first one was discovered in mid-April.
The flare-up has raised concerns over the fate of a ceasefire between Israel and Hamas, the Islamist rulers of Gaza, that has held since the 50-day war left more than 2,251 Palestinians and 73 Israelis dead.
- 'Breakthrough' in tunnel finding -
Israeli army spokesman Lieutenant Colonel Peter Lerner said the new tunnel discovered Thursday had been about 30 metres (100 feet) deep.
The army would continue to act along the disputed border region.
"We see Hamas are continuing to try and build this infrastructure into Israel and it is something we are not prepared to tolerate," said Lerner.
Israeli media have reported a major technological advance in Israel's ability to detect Hamas tunnels, with Prime Minister Benjamin Netanyahu last month hailing the "breakthrough in the ability to locate tunnels".
The army has kept the nature of the alleged technology secret and Lerner refused to elaborate.
Mahmud Atawnah, 29, from Jabalia area of northern Gaza, was taken into custody at the beginning of April after crossing the border fence into Israel, it said, adding he had provided "a lot of information on the Hamas tunnel industry".
The army also established a closed military zone around the small Israeli border town of Nahal Oz on Wednesday, saying troops had been fired on in the area.
Gaza has been devastated by three conflicts between Israel and its Hamas rulers and other Palestinian factions since 2008, and reconstruction has been painstakingly slow amid an Israeli blockade on all imports that could have military purposes.
- 'No interest in escalation' -
Although renewed violence has raised fears of a fresh conflict, sources on both sides downplayed the danger.
"Israel has no interest in escalation whatsoever," Lerner said.
Mustafa al-Sawaaf, former editor at the Hamas-affiliated Palestine newspaper, said the Islamist movement was not looking for a wider conflict.
"What happened are feelers and will not lead in the near future to a showdown between the resistance and the occupation," he said, saying Hamas was sending a message to Israel to stop its incursions.
"I think the message has been delivered."
On Thursday, Israeli General Yoav Mordechai denied reports about a cease-fire agreement between the sides.
"The army intends to maintain its activities against Hamas as it continues to breach Israeli sovereignty and build tunnels," he said in a statement.
The border region has remained relatively quiet since 2014, despite allegations by the army that Hamas is building new tunnels from the enclave that could reach into Israel.
Most of the sporadic rocket fire from Gaza has been attributed to fringe Islamist groups challenging Hamas's authority, although Israel holds Hamas responsible for all fire from the territory and routinely responds with attacks on its positions.