However, Israel rejected at least two major elements of the ceasefire terms outlined by the Islamist movement, and fighting continued, albeit with less intensity than yesterday.
The inauguration of new US President Barack Obama on Tuesday is being seen by some as the time by which Israel will bow to mounting international pressure and call off its attacks.
At least three rockets landed in Israel from Gaza, the army said. Israeli air strikes killed four Palestinians, three of them guerrillas and one a civilian, medics and militants said.
"Hopefully we're in the final act," Prime Minister Ehud Olmert's spokesman Mark Regev said, adding that briefings by the envoys working in Washington and Cairo on Friday could be followed by swift decisions by the security cabinet.
Such decisions could come by Saturday, Israeli officials said, as Palestinians in the Gaza Strip savoured a relative lull after intense combat on Thursday that many had seen as a final Israeli push before agreeing to ceasefire terms.
"The conditions have not come to fruition yet," security cabinet member Binyamin Ben-Eliezer said. "But this could well happen late on Saturday and we can put this story behind us."
Hamas rocket fire was more limited than before. It was far from clear if that was significant but the end of rocket fire was Israel's main demand in launching its offensive on Dec. 27.
After another uneasy night on which Israeli aircraft struck 40 targets in the crowded coastal enclave, Friday morning dawned relatively quiet on a population stunned by the extent of advances by Israeli tanks into the city of Gaza on Thursday.
Diplomats have spoken with growing confidence that some kind of ceasefire will be arranged in the coming days and suggested that Israel had been making a last push against its Islamist enemies before a deal was brokered.
An Israeli air strike on Thursday killed one of Hamas's top leaders, Saeed Seyyam, the interior minister in Gaza's unrecognised government and leader of 13,000 armed security men. Nine other people were killed in that bombing.
Israeli Foreign Minister Tzipi Livni, whose prospects in a Feb. 10 election may have been improved by the short war costing no more than 13 Israeli lives, was to hold talks on Friday in Washington with the outgoing administration of George W. Bush.
US Secretary of State Condoleezza Rice told outgoing Israeli Prime Minister Ehud Olmert that Washington, his most important ally, would commit in writing to steps to prevent Hamas from rearming through smuggling tunnels from Egypt, the Jewish state's main condition for a lasting ceasefire.
Egypt is mediating between Israel and Iranian-backed Hamas, which is shunned by Israel and its Western allies for its refusal to abandon an objective of destroying the Jewish state by force and establishing an Islamist state in all of what was Palestine before the creation of Israel in 1948.
Amos Gilad, a senior Israeli official, was heading to Cairo again on Friday. "When we are briefed by Gilad and Livni, there may be a full security cabinet meeting and decisions will stem from that," Regev said.
Hamas and diplomatic sources told Reuters on Thursday that Hamas had offered a one-year, renewable truce on condition that all Israeli forces withdrew within a week and that all the border crossings with Israel and Egypt would be opened.
Except for limited humanitarian supplies, the crossings have been all but closed under an Israeli-led blockade since Hamas seized control of Gaza in 2007 from forces loyal to Palestinian President Mahmoud Abbas of the Fatah faction. Hamas had won a Palestinian parliamentary election the previous year.
Israeli and Western sources, speaking to Reuters on condition of anonymity on Friday, said Israel has objected to putting a time limit on the truce.
"A time limit ... is a mistake," a senior Israeli source said, noting how a six-month truce last year ended in violence.
Another major Israel counter-demand to Hamas is that Abbas's forces staff crossing points, as they did before Hamas took over Gaza. Hamas and Fatah are bitterly at odds, adding to Abbas's many difficulties in negotiating a peace settlement with Israel that would give Palestinians a state in Gaza and the West Bank.
Analysts saw a possible deadline for the offensive with the departure of the Bush administration, after which Israel may be reluctant to test the support of the new leadership.
UN Secretary-General Ban Ki-moon, on a peace mission to the Middle East, said on Thursday the Israeli government was due to make an important decision on a ceasefire but that it might take "a few more days".
Ban also condemned as an "outrage" an Israeli attack on a UN storage compound in Gaza which destroyed desperately needed food supplies.
Launched on Dec. 27 with the stated objective of ending Hamas rocket attacks on Israel, the Israeli offensive has killed some 1,109 Palestinians and wounded 5,100, the Gaza Health Ministry said. A Palestinian human rights group put the civilian death toll at around 700.
