Hamas officials have also been in Cairo for talks with Egyptian negotiators.
"The movement has presented a detailed vision to the Egyptian leadership so that it (Egypt) can continue its pursuit to end the aggression and lift the injustice on our people in the Gaza Strip," Hamas official Salah al-Bardawil said.
These details concerned how to ensure that border crossings into Gaza could be re-opened under international supervision, he said, and would be presented to Israeli envoys visiting Cairo on Thursday.
A senior Israeli defence official, Amos Gilad, is to travel to Cairo on Thursday, a spokesman for Israeli Prime Minister Ehud Olmert said.
Earlier on Wednesday, other Hamas officials had said the Egyptian initiative had been positively received but that more time was needed to discuss it.
Hamas, which controls Gaza, has said any ceasefire agreement would have to entail a halt to Israeli attacks, a complete withdrawal of Israeli forces and the opening of border crossings to end the blockade of Gaza.
BBC Arab affairs analyst Magdi Abdelhadi says Israel will not agree to a deal that does not guarantee an end to Hamas's smuggling of weapons across the Egyptian border and the cessation of rocket attacks into southern Israel.
For its part, Hamas refuses to accept an agreement that could in effect spell the beginning of the end for its military wing.
Egypt and other key Arab states can put pressure on Hamas but the US remains unwilling to press Israel to make any concessions, our correspondent says.
'Seeds of extremism'
Israel launched its campaign against Gaza on 27 December, saying it wanted to end Palestinian rocket fire into Israel.
Syrian president on Gaza conflict
Both Hamas and Israel rejected last week's UN Security Council resolution calling for an immediate ceasefire.
The Israeli offensive has provoked widespread international condemnation at the cost in civilian casualties.
Bolivian President Evo Morales said he was cutting relations with Israel over what he called the "genocide" in Gaza.
President Bashar al-Assad of Syria warned that Israel's campaign would fuel extremism and terrorism in the Arab and Muslim world.
"The effect of war is more dangerous than war. It is sowing seeds of extremism around the region," Mr Assad said in an exclusive BBC interview.
On Wednesday, Israel continued to bombard the Gaza Strip and residents spoke of heavy machine-gun fire as Israeli troops fought Hamas gunmen near Gaza City.
Israeli strikes on Gaza continue
Meanwhile, three rockets were fired from southern Lebanon towards the northern Israeli city of Kiryat Shmona, landing on open ground.
No casualties or damage were reported.
In another development, a newly-released audiotape said to feature the voice of al-Qaeda leader Osama bin Laden has called for a holy war to stop the Israeli offensive in Gaza.
The authenticity of the tape, posted on a number of Islamic militant websites, could not be independently verified.
Humanitarian concerns have increased amid the fighting, although some aid is getting through to Gaza during daily three-hour lulls Israel has allowed to let in supplies.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.