Bar Rahav, 21, and Bnaya Rubel, 20, were killed respectively by an anti-tank missile and in a gun battle, both late Saturday, the army said, as Israel intensified its ground assault against the Palestinian territory.
The army gave no further details about the circumstances surrounding their deaths.
The armed wing of Hamas, the main target of Israel's operation, claimed in a statement early Sunday it had lured Israeli troops and tanks into an ambush in a mine field east of Gaza City, killing 14 soldiers.
An army spokeswoman had no immediate information on the incident.
Also on Saturday, Sergeant Adar Bersano, 20, from Nahariya, and Major Amotz Greenberg, 45, from Hod Hasharon, were killed fighting a group of militants who infiltrated Israel through a tunnel from the centre of the Gaza Strip.
Hamas's military wing, the Ezzedine Al-Qassam Brigades, said 12 of their men stayed "behind enemy lines" for six hours before engaging in "direct confrontation with the enemy to avenge the blood of our martyrs, particularly the children."
The militants claimed they "killed six soldiers on patrol and wounded several others," but the Israeli army said there were only two deaths.
Israel's army announced it would expand its ground operation, which began late Thursday, 10 days into military campaign.
Chief-of-Staff Lieutenant General Benny Gantz warned Friday that as Israel expanded the ground operation there would be "moments of hardship," alluding to the possibility of further Israeli casualties.