Gaza City (CNN) -- A delegation from Gaza was in Egypt Monday to hash out more details of a cease-fire deal between Hamas and Israel, less than a week after the truce ended an eight-day conflict.
The continued talks are a key part of the agreement, which called for "total cessation of all hostile activity" and discussion of topics such as opening border crossings and easing Israel's economic blockade in Gaza.
While new negotiations were under way in Egypt Monday, there were reports of violence along the Gaza-Israel border.
Hamas police and ambulance operators said Israeli soldiers injured two civilians when they fired at Palestinian homes east of Rafah City in Gaza. An Israeli military spokesman said the soldiers fired warning shots in the air and later shot toward the legs of "Palestinian rioters" who were damaging a security fence at the border and trying to enter Israel.
The Israeli military said earlier that it was investigating a stabbing Monday near the border. Israeli soldiers killed a man who infiltrated the village of Sde Avraham from Gaza and stabbed a woman, who was lightly injured, the Israel Defense Forces said.
The fragile truce between Israel and Hamas has appeared to hold up despite such flareups.
On Friday, there were reports that Israeli troops shot and killed a Palestinian man near the border. Fighting also was recorded Thursday, a day after the cease-fire was declared.
Egypt and the United States helped broker the cease-fire last week after Israel launched a series of military strikes on Gaza with the stated goal of halting Israel-bound rocket attacks from militants in the Palestinian territory.
Egyptian President Mohamed Morsy helped forge the cease-fire, as Israeli forces gathered near the Gaza border for a possible ground invasion.
On Monday, Morsy was facing a political crisis in his own country, with some protesters calling him a dictator and judges striking nationwide in protest of the president's announcement last week that Egyptian courts cannot overturn the decisions or decrees he's made since taking office in June.
It was unclear whether the turmoil in Egypt would affect the cease-fire talks.
The Gaza-Israel conflict left more than 160 Palestinians dead, many of whom were civilians.
The brother of BBC journalist Jihad Misharawi, whose 11-month-old son was killed in an Israeli airstrike, died from wounds suffered in the strike, medical sources said Monday.
Six Israelis also have died during the conflict, including civilians and soldiers.
The ongoing talks over the cease-fire deal come as Palestinian Authority leaders plan to make a pitch this week to become a non-member observer state at the United Nations.
"All the Palestinian factions are behind us as we go ... to the United Nations," Palestinian Authority President Mahmoud Abbas told supporters Sunday.
Hamas added its support Monday, an apparent change in position after stating a day earlier that there was "no truth" to reports that Haniyeh's office "has blessed the move to go to the United Nations."
The shift followed a phone call between Hamas political leader Khaled Meshaal and Abbas, according to the Hamas website.
The Gaza-based Hamas has long opposed the gambit that Abbas launched last year.
A vote on the Palestinian status is expected at the U.N. General Assembly on Thursday.
CNN's Kareem Khadder, Amir Ahmed and Michael Schwarz contributed to this report. Editor's Note: A U.N. report published on March 6, 2013, raises questions about who fired the rocket that killed the son and brother of Jihad Misharawi.