(Corrects day of Obama inauguration to Tuesday, paragraph 6)

* Israeli envoys head to Washington, Cairo

* At least 1,105 Palestinians dead as war nears fourth week

* Hamas interior minister killed

* U.N. warehouse hit by Israeli air strike

By Nidal al-Mughrabi

GAZA, Jan 16 (Reuters) - Israel said its Gaza offensive could be "in the final act" on Friday as it despatched envoys to discuss truce terms after Hamas made a ceasefire offer to end three weeks of fighting that has killed more than 1,100 people.

"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 be made on Friday or 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 Israeli army said that, for the first time in weeks, no rockets had landed in Israel from Gaza. It was far from clear if that was significant but the end of rocket fire was Israel's key 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 -- possibly in time for the inauguration of the new U.S. president Barack Obama on Tuesday.

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.

WASHINGTON VISIT

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.

U.S. Secretary of State Condoleezza Rice has told outgoing Israeli Prime Minister Ehud Olmert that Washington, his key ally, is prepared to offer some form of guarantee to meet the Jewish state's demand that any under lasting ceasefire Hamas will be unable to rearm through smuggling tunnels from Egypt.

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," Olmert's spokesman Regev said.

Israeli officials said the security cabinet could meet as early as Friday or on Saturday.

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.

They 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.

Israel has been pressing for a permanent or much longer ceasefire and is likely to resist Hamas's demands for an international conference on reconstruction and for the exclusion of Abbas's forces from their former role at border crossings.

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.

U.N. ANGER

U.N. 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 U.N. 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 1,105 Palestinians and wounded 5,100, the Gaza Health Ministry said. A Palestinian human rights group put the civilian death toll at around 700.

Despite world outcry over the carnage and damage to media and U.N. aid facilities, Israel has vowed to fight on until the rocket salvoes stop and measures are imposed to stop Hamas bringing in arms via tunnels from Egypt.

What that might entail is unclear as Cairo rejects Israeli allegations that it has not cracked down on the weapons shipments and has been publicly reluctant to allow international forces to help supervise the sandy 15 km (9 mile) frontier.

Israeli warplanes have bombed the border corridor and defence officials hinted troops could move in -- though that might clash with Israel's assertion that, having quit Gaza in 2005 after 38 years of occupation, it has no plan to return.

Israelis also face a Feb. 10 election which will pit Livni, Defence Minister Ehud Barak and opposition leader Benjamin Netanyahu against one another, straining the cross-partisan support that the offensive has enjoyed so far.

About 25 rockets fired from Gaza hit southern Israel on Thursday, wounding six people. Such salvoes have killed three Israeli civilians and a soldier during the offensive. Nine troops have died during fighting centred in northern Gaza.

Hamas's Damascus-based leader Khaled Meshaal reiterated his group's demands: "First, the aggression must stop; second, the Israeli forces must withdraw from Gaza...immediately, of course; thirdly, the siege must be lifted and fourth we want all crossing-points reopened, first of which is Rafah (Egypt)." (Additional reporting by Adam Entous in Jerusalem; writing by Alastair Macdonald; editing by Philippa Fletcher)

AlertNet news is provided by