The Israeli military said soldiers opened fire after spotting three suspicious figures approaching the border fence near the Israeli village of Nahal Oz.
Israeli army radio reported that the men were trying to reach a bomb planted near the fence.
However, Palestinian officials said the men were border policemen on patrol who were fired on by machine guns mounted on Israeli tanks.
Palestinian hospital sources said the men were hit by fragments of a tank shell.
On Monday an Israeli missile strike on a car in the northern Gaza Strip killed two Palestinian militants and wounded three others.