A gun battle has erupted between Hamas militants and Israeli troops in Gaza in one of the worst clashes since Israel launched an offensive there on Tuesday.
Israel remains poised to enter the north of the Gaza Strip
Israeli tanks and bulldozers crossing the border near Khan Younis ran into gunfire and grenades.
Israeli forces are already in the south of Gaza as part of pressure to free a soldier captured by militants.
US President George W Bush has said the release of Cpl Gilad Shalit is key to resolving the crisis.
Israel has rejected conditions set for information on, or the freeing of, the tank gunner who was seized in a raid on his border post last Sunday in which two other soldiers and two attackers died.
The three groups believed to be holding him have demanded the release of 1,000 prisoners held in Israeli prisons, and an end to the offensive.
A large Israeli force remains poised on Gaza's northern edge as mediators make last-ditch attempts to reach a solution.
There were no reports of casualties in Saturday's battle.
It was the first sustained encounter between the two sides since the incursion was launched on Tuesday night, the BBC's Alan Johnston reports.
A small force of tanks and bulldozers had crossed the Israeli border in what the Israelis say was a limited operation and they were attacked after moving only a few hundred metres.
One grenade reportedly struck a bulldozer.
According to French news agency AFP, the Israelis responded with artillery and helicopter gunships.
An AFP reporter saw more gunmen heading for the fight armed with mines and rockets.
There have been four consecutive nights of air strikes, targeting what the Israelis say are Palestinian militant positions.
However, casualties in Gaza have been relatively light since the incursion began, with the deaths of two militants reported.
Mr Bush said the release of the soldier was key to ending the crisis which has seen Israeli forces destroying Gaza bridges and suspected militant sites, as well as the strip's only power station.
GAZA CRISIS TIMELINE
Sun 25 June: Cpl Gilad Shalit captured in cross-border attack
Mon 26 June: Palestinian Popular Resistance Committees demand prisoner releases in exchange for Shalit
Weds 28 June: Israeli military enters southern strip after launching air strikes on Gaza
Thurs 29 June: Israel detains dozens of Hamas officials
Sat 1 July: Groups believed to be holding Cpl Shalit demand 1,000 prisoners be released
"The initial goal should be freeing the Israeli soldier - that is the key to ending the crisis," President Bush was quoted by the White House as saying.
He was speaking in a phone call with Prime Minister Tayyip Erdogan of Turkey.
There are conflicting reports about whether the soldier has been visited by a doctor.
A spokesman for the Popular Resistance Committees, one of the groups believed to be holding Cpl Shalit, told the BBC there was no truth to a Fatah report he had been given medical treatment.
The head of Egyptian intelligence, Omar Suliman, is due to arrive in the region on Saturday for talks with both Palestinians and Israelis.
Mahmoud Abbas, the Palestinian president whose allies lost to Hamas in the January parliamentary election, has apparently accused Hamas of failing to present a united negotiating front.
"Hamas's political leadership outside are saying the decision is in the hands of its military wing... while the military wing is saying the decision is in the hands of the political leadership outside," he was quoted as saying in a statement by The Associated Press.