Secretary of State Condoleezza Rice elaborated the position after a meeting of the International Quartet that called for intensified Middle East peace talks but offered no new initiative to follow up on Israel's pullout from Gaza.
At a news conference on Tuesday, Rice reiterated the US view that there was a "fundamental contradiction" between Hamas' armed activities and its plan to run in January's legislative polls.
But she added: "We understand that the Palestinian political system is in transition, that it is in transition towards a democratic system and that that has to be a Palestinian process.
"I think we have to give the Palestinians some room for the evolution of their political process," the chief US diplomat said.
Israeli Prime Minister Ariel Sharon has threatened to withhold all cooperation in election preparations if Hamas, considered by his country and the US as a terrorist group, is allowed to run.
By contrast, Rice said: "We would hope that the elections can go forward and that everyone will cooperate to make those elections go forward because elections are fundamental to the continued evolution and development of the Palestinian process."
The comments by Rice appeared softer than those of the White House, which vowed 11 days ago to boycott Hamas members elected to the Palestinian parliament in January.
Rice is hopeful that Palestinian
elections will go forward
"We do not believe that, in the end, a democratic state can be built when parties or candidates seek power not only through the ballot but through terrorist activities as well," said National Security Council spokesman Fred Jones.
Rice held her first meeting with Quartet partners from the United Nations, European Union and Russia since the Gaza handover, which they called an opportunity to revive work on their road map for peace.
"Contacts between the parties should be intensified at all levels," they said in a statement. It urged "renewed action in parallel by both parties" on their obligations under the road map aimed at creation of a Palestinian state.
The Palestinians have expressed fears that the Israelis would use the success of their Gaza withdrawal as cover to avoid similar moves to pull out of the West Bank.
Not ripe time
But UN Secretary-General Kofi Annan acknowledged the time might not be ripe for any major moves, with Sharon facing a serious political challenge and the Fatah movement of Palestinian leader Mahmoud Abbas in a showdown with Hamas.
"Obviously we are monitoring these events very closely and would want to see that settled before one takes any other bold initiatives," Annan told the news conference.
"For us, the Quartet, it's Gaza first and then the next stage will be West Bank, not Gaza first and Gaza last"
"But what happens in the West Bank is very much on our mind. For us, the quartet, it's Gaza first and then the next stage will be West Bank, not Gaza first and Gaza last."
A Palestinian Authority spokesman said Rice called Abbas on Tuesday to inform him of progress in the Quartet's quest for peace.
"Rice called Abbas to inform him of efforts to be made so that the Israeli withdrawal from the Gaza Strip will be followed by initiatives that will allow the creation of a Palestinian state," Nabil Abu Rudeina told AFP in Gaza.