Talks between US Secretary of State Condoleezza Rice and senior Israeli and Palestinian negotiators over border crossings have continued overnight.
Rice has met both Ariel Sharon and Mahmoud Abbas
Ms Rice met both parties separately throughout the night at a hotel in Jerusalem working on the deal.
She had delayed her departure to Asia as the possibility of a breakthrough grew to open Gaza's border with Egypt.
The secretary of state had expressed hope that a deal was in sight but there was still no word on an agreement.
"Will and some creativity" could result in a deal, Ms Rice said on a visit to Ramallah in the West Bank, on Monday.
Earlier Israeli troops killed a militant in Gaza and another in the West Bank.
The army said they had opened fire when they saw gunmen near the Israeli-built Gaza border fence, killing one and wounding two others.
In Nablus, in the West Bank, troops on an arrest operation killed a local Hamas commander.
Ms Rice is on her fourth visit to the region this year, and her first since Israel withdrew soldiers and settlers from the Gaza Strip in September.
She had been due to fly to Pusan in South Korea for an Asian regional conference.
On Monday, she held talks with Israeli and Palestinian leaders on reviving the peace process.
"What is needed is some agreement on how to improve freedom of movement" for Palestinians living in Gaza, she said after meeting Palestinian leader Mahmoud Abbas.
Israel maintains tight controls on passage in and out of the narrow coastal strip that is home to more than a million Palestinians.
Mr Abbas has blamed the Israelis for delaying an agreement.
The Americans had hoped that Israel's Gaza withdrawal would significantly improve the prospects for peace but in fact relations have worsened, the BBC's Alan Johnston in Jerusalem says.
Although the Israelis have pulled out of Gaza, they have tightened their hold on all its routes to the outside world.
They say they must guard against the threat of militant attacks emerging from the territory.
During her stay in Jerusalem, Ms Rice attended a memorial for Yitzhak Rabin at Mount Herzl cemetery to mark the 10th anniversary of the former prime minister's assassination according to the Hebrew calendar.
Her trip came amidst an Israeli political crisis, with the new leader of the Labour party demanding fresh elections.
Another top-level envoy, James Wolfensohn, said Gaza could be turned into a jail unless border crossings were fully opened.
Mr Wolfensohn (left) is concerned about Palestinian agriculture
The situation threatened to deepen Palestinian unemployment, he said in Jerusalem.
But Mr Wolfensohn, who speaks for the UN, Russia, the EU and the US, added that there had been several incidents of explosives being smuggled in trucks headed to Israel.
Before meeting Israeli PM Ariel Sharon on Monday, Ms Rice said a Palestinian state would "enhance Israeli security".
Mr Abbas pledged that Palestinian elections would go ahead as planned in January, and would "show we have chosen a democratic path" towards a state that could live in peace with Israel.