Israeli military confirmed an officer and a soldier had been killed and two soldiers injured on Friday.
Ban Ki-moon, the UN secretary-general, said on Saturday that he was concerned about Friday's clash in the Gaza Strip.
"I am very concerned at the escalation of violence and loss of life yesterday in the vicinity of the Gaza border," Ban told a news conference held on the sidelines of an Arab League summit in the Libyan town of Sirte.
"I reiterate my appeals made during my recent visit for maximum restraint and an end to all violence, in particular at this critical time when we are engaged in efforts to revive peace talks."
Izz al-Din al-Qassam Brigades, the armed wing of Hamas, said it engaged the Israeli military after the incursion.
"An Israeli army force raided 500 metres into Palestinian territory, and was confronted by our gunmen," Abu Obeida, a Hamas spokesman, said.
"This was our work, but was carried out for defence."
Al Jazeera's Barnaby Phillips, reporting from Gaza, said that the situation "does seem to have improved" but that it was "certainly tense".
"There was a fair amount of helicopter and drone activity over the skies above Gaza last night," he said.
"The Israelis are saying that a rocket was fired out of Gaza into Israel this morning, [but] no group has claimed responsibility for it. It landed in open ground and didn't cause any harm to anybody."
Our correspondent said he had spoken to Hamas officials who said that "this is not the time to try and draw the Israelis into a larger conflict".
"They recognise that people in Gaza want peace at the moment above all," he said.
The correspondent added that a 23-year-old Palestinian who had been wounded in the clashes had died of his wounds.
Responding to the Israeli deaths, Israel's defence minister issued a veiled threat to Hamas.
"We have been used to seeing breakaway [Palestinian] groups doing the firing, and Hamas trying to calm things down. Possibly it is loosening its grip, for all sorts of reasons," Ehud Barak told Israeli television on Friday.
"Should that indeed prove to be the case, and then there will also be ramifications for Hamas," he said, but added: "We have no interest in returning the region to what was in the past."
Some witnesses said Friday's exchange of fire began when an explosion, possibly caused by an anti-armour rocket fired from the nearby Palestinian town of Khan Younis, hit an Israeli army patrol on the central Gazan border.
Backed by tanks, the troops fired back at their assailants and entered Gazan territory, the witnesses said.
Such pursuits are common practice for the Israelis, who try to maintain a buffer zone within the border fence off-limits to Palestinians.