"The man was armed with a Kalashnikov automatic assault rifle and a combat vest," the military statement said.
There was no immediate comment on the incident from the Palestinian side.
Meanwhile Egypt has continued to act as a mediator as it attempts to solve the week-old crisis at the Gaza-Egyptian border and work out a compromise between Abbas and Hamas.
Hundreds of thousands of Palestinians flooded into Egypt to buy essential supplies previously denied them by an Israeli blockade of the territory.
Egypt increased security around the border town of Rafah on Tuesday, and resealed parts of the barrier destroyed a week ago by Hamas fighters, in an attempt to control the flow of people in and out of the Gaza Strip.
Egyptian state media has reported Cairo is soon to close the border.
One state-run newspaper said Cairo planned to close the border on Thursday, and the al-Ahram newspaper said the last opportunity for Gazans to return home would be at the start of next week.
The situation for the Gaza Strip, however, remains unresolved, and the Israeli Supreme Court upheld the government's decision to cut fuel and electricity shipments.
Israeli human rights groups have challenged the sanctions, which Israel says are aimed at halting ongoing rocket fire by Gaza fighters.
Palestinian officials say the cutbacks have harmed Gaza's already impoverished residents by causing power shortages and crippling crucial utilities.
Israel, which pulled out of Gaza in 2005 after a 38-year occupation, supplies all of Gaza's fuel and more than two-thirds of its electricity.
The Israeli blockade of the strip, appeared to be easing, however, when Asher Luk, the manager of Israel's Karni crossing with Gaza, said that 70 trucks of wheat and animal feed would be allowed into the Gaza Strip on Wednesday and Thursday.
Since Israel and the Palestinians revived their peace negotiations in late November, following a seven-year freeze, at least 145 people, mostly armed men, have been killed by Israeli troops in Hamas-run Gaza.
Meanwhile, hundreds of rockets have been fired into Israel from the northern end of the Strip.
Thursday's death brings to 6,105 the number of people killed since the start of the second Palestinian uprising in September 2000, vast majority of them Palestinians.