Officials from Hamas have blamed the killing, in Khan Younis, on the rival Fatah faction.
The truce went into effect early Tuesday 3 a.m. local time and appeared to be taking hold after five days of intense fighting.
Previous ceasefire deals between Hamas and Fatah quickly broke down.
In Egypt today for talks with President Hosni Mubarak, Palestinian President Mahmoud Abbas, of Fatah, called for the abolition of a large Hamas militia, the Executive Force.
Mr. Abbas also condemned a Palestinian suicide bombing Monday in the Israeli city of Eilat that killed three Israelis.
Israel says the bomber, from the Gaza Strip, crossed into Eilat from Egypt.
Israeli officials say they are planning to step up security on the Egyptian border. Some Israeli officials have hinted at possible military retaliation for the bombing.
Meanwhile, Israeli forces bombed a tunnel on the Gaza-Israel border they say was going to be used by Palestinian militants to attack Israel.
The Palestinian factions Hamas and Fatah have been locked in a power struggle since Hamas defeated Fatah in parliamentary elections one year ago.
The violence has derailed efforts to form a unity government. More than 30 people, including several children, were killed in the past five days of Palestinian fighting in the Gaza Strip.
Information for this report is provided by AP, AFP and Reuters