GAZA (Reuters) -- Israel has said its Gaza offensive could be "in the final act" and sent envoys to discuss truce terms after Hamas made a cease-fire offer to end three weeks of fighting that has killed more than 1,100 Palestinians.
However, Israel rejected at least two major elements of the cease-fire terms outlined by the Islamist movement, and fighting continued, albeit with less intensity than on January 15.
The inauguration of new U.S. President Barack Obama on January 20 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 January 16 could be followed by swift decisions by the security cabinet.
Such decisions could come by January 17, Israeli officials said, as Palestinians in the Gaza Strip savored a relative lull after intense combat on January 15 that many had seen as a final Israeli push before agreeing to cease-fire 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 December 27.
After another uneasy night on which Israeli aircraft struck 40 targets in the crowded coastal enclave, the morning dawned relatively quiet on a population stunned by the extent of advances by Israeli tanks into the city of Gaza on January 15.
Diplomats have spoken with growing confidence that some kind of cease-fire 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 January 15 killed one of Hamas's top leaders, Said Seyyam, the interior minister in Gaza's unrecognized government and leader of 13,000 armed security men. Nine other people were killed in that bombing.
Russia Seeks Help Of Syria, Iran
Meanwhile, Russia has asked Iran and Syria to help persuade Hamas to accept the Egyptian proposal on ending the fighting in Gaza, Russian Foreign Minister Sergei Lavrov has said.
"Egypt's initiative...is, for us, optimal and we believe all efforts should be thrown into supporting it," Lavrov told a news conference.
"In connection with this we are sending corresponding signals to representatives of Hamas, and those states which have influence on Hamas," he said.
"First and foremost that is Iran and Syria. We have spoken to our colleagues. I hope that everyone will concentrate on this."
Russia maintains close ties to Tehran and Damascus and has official contacts with Hamas, which is shunned by Western powers for refusing to abandon its objective of destroying the Jewish state.