A group of Palestinian fishermen was also shot at by Israeli warships on Wednesday. Three fishermen were wounded.
Abbas and Ehud Olmert, Israel's prime minister, declared the ceasefire on November 26 in what they described as a bid to restart peace efforts.
"What has been achieved so far is a tremendous loss of Palestinian lives to no foreseeable avail"
Tribunus, Madison, USA
Send us your views
Palestinian fighters in Gaza have fired about 20 rockets into Israel during the truce, causing no casualties.
Medics have said previously that at least three Palestinians have been wounded by Israeli fire since the start of the truce.
The Israeli army says it shot one man who was allegedly tampering with the security fence on the Israel-Gaza border.
Since the Gaza ceasefire came into effect, Israel has launched several raids in the occupied West Bank, where there is no truce.