In the first attack, the troops shot dead a 60-year-old woman in a refugee camp and wounded four other Palestinians.
Witnesses and medics said the shooting occurred as Israeli tanks took up positions on the edges of the Khan Yunis camp on Monday.
Israeli military sources said its forces had moved in during an operation against "terrorist infrastructure", but did not elaborate.
Palestinian security sources said three tank shells were also fired into the camp and that Israeli troops used machine guns from helicopters.
However, an Israeli army spokesman said the machine-gun fire was intended to prevent Palestinian resistance fighters from approaching the tanks.
Israeli troops shot dead three
Palestinians in Gaza
In the second attack, in the northern part of the Gaza Strip, Israeli occupation forces opened fire on three Palestinians, killing them.
Israeli military sources alleged Palestinians were approaching an illegal Jewish settlement.
Violence has surged in the Gaza Strip as Israeli forces prepare to remove troops and colonists in a pullout that Israeli Prime Minister Ariel Sharon plans to complete by the end of 2005.
An internal Palestinian power struggle has also spilled over into lawlessness and has been marked by demands for President Yasir Arafat to carry out anti-corruption reforms in his Palestinian Authority and security forces.