Ms Rice said Hamas was a "terrorist organisation"
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The United States has said it is "deeply troubled" by Israel's killing of Hamas leader Sheikh Ahmed Yassin.
However, officials made no formal condemnation of the attack and denied any advance knowledge of Israeli plans to target the Hamas leader.
State department spokesman Richard Boucher said Israel had the right to defend itself against terror attacks.
But Mr Boucher said the assassination would not help efforts to resume the peace process.
Mr Boucher said Washington was "deeply troubled by this morning's
events".
He added: "We do think that this event increases tension
and it doesn't help efforts to resume progress towards peace."
The BBC's Rob Watson in Washington says there is unlikely to be any outright condemnation of the attack from the Bush administration, because it has already said it considers Hamas a terrorist group.
But the events in Gaza have clearly put the administration in an awkward spot as it tries to reconcile its strong opposition to Hamas with its disapproval of what it calls "targeted killings" by the Israelis, our correspondent says.
The White House issued an appeal for restraint on all sides.
White House National Security Adviser Condoleezza Rice appealed for calm: "It is very important that everyone step back now and try now to be calm in the region," she told NBC's Today show.
Our correspondent says that what the Americans are hoping is that the killing is one last show of strength by Israeli Prime Minister Ariel Sharon that may be a prelude to pulling out of Gaza.
'Hamas are terrorists'
The US, Russia, the European Union and the United Nations are the joint authors of the "roadmap" peace plan that envisages a Palestinian state alongside Israel.
Given the immense wave of anger, the prospect of restarting peace talks between Israel and the Palestinians now seems even more remote, says the BBC's David Chazan in Gaza.
Ms Rice said she hoped nothing would be done that would ruin the chances of new opportunities for peace in the Middle East.
"There is always a possibility of a better day in the Middle
East and some of the things that are being talked about by the Israelis about disengagement from areas might provide new opportunities," she said.
But she added: "Let's remember that Hamas is a terrorist organisation and that Sheikh Yassin has himself personally, we believe, been involved in terrorist planning.
"But of course the United States did not have advanced warning," she said.