JERUSALEM — Israel plans to pull all of its troops out of the Gaza Strip by the time President-elect Barack Obama is inaugurated Tuesday, but only if Hamas militants hold their fire, Israeli officials said.

Thousands of troops have left Gaza since Israel declared Saturday its intention to unilaterally halt fire after a devastating, three-week onslaught. Gaza's Hamas rulers ceased fire 12 hours later. Large contingents of Israeli soldiers have kept close to the border, prepared to re-enter the territory if violence reignites.

A swift troop withdrawal would reduce the likelihood of clashes between militants and Israeli forces that could rupture the truce.

By getting its soldiers out before the Obama inauguration, Israel hopes to pave the way for a smooth beginning with the Obama administration and spare the incoming president the trouble of having to deal with a burning problem in Gaza from his first day, the Israeli officials said.

They spoke on condition of anonymity because they were not authorized to speak publicly about the plan.

Israel has been quietly concerned about possible policy changes by the incoming administration after eight years of staunch support from President George W. Bush. Obama has said Mideast peace will be a priority even as he grapples with a global economic crisis and wars in Iraq and Afghanistan.

Israel made its troop withdrawal plan known at a dinner Sunday with European leaders who came to the region in an effort to consolidate the fragile cease-fire.

Prime Minister Ehud Olmert told his guests that his country had no desire to stay in Gaza, a Mediterranean strip of 1.4 million people that Israel vacated in 2005, while retaining control of its airspace, coastal waters and border crossings.

"We didn't set out to conquer Gaza. We didn't set out to control Gaza. We don't want to remain in Gaza and we intend on leaving Gaza as fast as possible," Olmert told the leaders of Britain, France, Germany, Spain, Italy and the Czech Republic.

Israel holds elections next month, and polls show Israel's wartime leaders have been strengthened by the offensive that drew overwhelming support at home even as it attracted widespread condemnation across the globe.