Officials on both sides said at least two Palestinians and two Israeli soldiers were killed, while two other Israeli soldiers were injured. Reports indicate civilians also were hurt.
The violence is among the worst in Gaza since Israel's offensive against Gaza at the end of 2008. Witnesses said the intense fighting kept ambulances from reaching the wounded.
The militant group Hamas said its members opened fire after Israeli forces crossed the border and advanced about 500 meters into Gaza. The Israelis said the first exchange of gunfire was with militants trying to plant explosives near a border fence.
Israeli officials said its troops were supported by tanks and helicopter gunships.
The Israeli military said in a statement that it holds Hamas "solely responsible" for maintaining peace in the Gaza Strip.
After the fighting broke out, some Hamas officials claimed Friday that they had lured the Israeli forces into an ambush. And some witnesses said the battle began after an explosion near the Israeli forces.
This is a development worth watching as violence continues to increase in the region.