The attack comes amid a surge in tensions among Palestinian factions after Abbas on December 16 announced he would seek early presidential and parliamentary elections.
At a Palestinian hospital, an unidentified soldier stood over the body of the slain guard.
"A training site for the presidential guard was attacked by a mortar," he said. "What kind of a justice is this? Where is Mahmud Abbas's decision? Where is the decision of the president? These attacks must be stopped."
At least 15 other people were reported injured in the attack. Armed, masked men -- including members of the presidential guard, the Fatah movement, and the Fatah splinter group al-Aqsa Martyrs Brigade -- were reportedly stopping and checking vehicles attempting to enter the area near Abbas' office and house.
Hamas and Abbas' Fatah movement have clashed on numerous occasions during this year, but this recent outbreak of fighting between the Palestinian groups was sparked by Abbas's December 16 announcement.
Two Heads Bad
Abbas justified his call for early legislative and presidential elections by saying the rivalry between Hamas and Fatah has made governing the Palestinian territories nearly impossible.
"They [Hamas] are supposed to help the president with his duties, not to stand in the president's way of performing his duties," Abbas said during his televised speech. "There are not two heads in town -- we don't have two heads in town. I signed a decree to create this government and I can sign a decree to fire it and this is my right."
Abbas said elections are the best way to resolve the power struggle between Hamas and Fatah. The battle for power started shortly after Hamas won a majority in parliament in elections in January this year. Since then Hamas and Fatah has not been able to form a unity government.
Hamas has already made clear it does not support President Abbas's decision to hold early elections.
"We are not going to participate or to allow the holding of an election, which is unacceptable," senior Hamas leader Mahmud Azzahar said shortly after the president's speech. "We are here running governments. The government will not arrange for any election and the central committee for the election should cooperate. If we are not going to cooperate, there will be, in practice, no election."
Senior members of Fatah have already indicated they will ask Abbas to run for reelection in any early elections.