President Shimon Peres of Israel on Sunday rejected the possibility of a cease-fire as Israeli forces continued an offensive against Hamas in the Gaza Strip.
But in an interview on the ABC News programme This Week, Mr Peres said Israel does not intend to occupy Gaza.
Meanwhile, Israeli troops backed by tanks battled Hamas fighters in Gaza City on Sunday.
Heavy fighting was also reported around the northern towns of Beit Lahiya, Beit Hanun and Jabaliya.
The BBC reports the territory has effectively been cut in two by the invasion. Gaza City is virtually surrounded.
The biggest Israeli military operation since a war in Lebanon in 2006 began on Saturday, 27 December. Ground forces entered Gaza on 3 January after a week of bombing.
A six month truce was ended by Hamas on 19 December. Gaza has a population of 1.5 million. Israel is to hold an election on 10 February.
Meanwhile, Hamas has kept up rocket salvoes against southern Israel.
International efforts to halt the conflict are so far unsuccessful with the UN Security Council unable to agree on the wording of a statement on the conflict.
A delegation from the European Union is due to begin a visit to the region on Sunday, but has acknowledged it faces a difficult task.
The head of medical emergency services in Gaza says the death toll to date is at least 500, with more than 2450 people wounded.
The leaders of the only two Arab countries that have peace treaties with Israel have both condemned the offensive.
Egypt says Israel should end its invasion immediately and without pre-conditions.
King Abdullah of Jordon says the attacks will not achieve security for Israel.
British Prime Minister Gordon Brown has again called for an immediate ceasefire.
He told the BBC on Sunday that this included Hamas ending its rocket attacks against Israel.
Mr Brown also said any solution would have to include stopping the supply of arms into the region and ensuring international monitoring.
He said he had spoken to the Israeli prime minister on three occasions in the past few days and had attempted to talk to Palestinian President Mahmoud Abbas and others in the region about what could be done.
Mr Brown said Arab powers had to apply pressure to ensure that illegal tunnels used for supplying Gaza with arms were closed.
United States Vice-President Dick Cheney has defended Israel's ground assault on Gaza, saying air attacks are not enough to destroy the sites where Hamas fires its rockets.
He said Israel did not seek US approval before sending in its troops.