US President George W Bush and Israeli Prime Minister Ehud Olmert have offered strong support for Palestinian Authority President Mahmoud Abbas.
The two leaders both described Hamas as "extremists"
Calling Mr Abbas "the president of all the Palestinian people", both men pledged to work with his new emergency government, which excludes Hamas.
Mr Olmert insisted he was ready to meet Mr Abbas on a regular basis.
Mr Bush and Mr Olmert met for private talks at the White House following the military takeover of Gaza by Hamas.
After meeting the media, the pair spoke for about 90 minutes, aides said, but there was no indication of what they discussed.
Mr Abbas sacked the Hamas-led Palestinian government in the aftermath of the takeover, replacing it with an emergency administration led by an independent.
Ahead of the Washington meeting a Hamas spokesman said the talks were aimed at destroying his organisation.
Elsewhere, Egypt, announced it would move its ambassador and other diplomats from Gaza to the West Bank town of Ramallah, where Mr Abbas' government sits.
Egypt repeatedly tried to mediate in the bloody battle between Fatah and Hamas in Gaza, but has since condemned the Islamist group's takeover.
Speaking before the start of private talks in Washington, both the US and Israeli leaders said Mr Abbas "speaks out for moderation" in the Palestinian territories.
"He is a reasonable voice among the extremists in your neighbourhood," Mr Bush said to Mr Olmert.
Mr Olmert condemned the "brutality" of Hamas, but said he would make every possible effort to co-operate with Mr Abbas, raising the prospect of bi-weekly meetings.
Mr Bush repeated his previously-stated commitment to the establishment of an independent Palestinian state, a sentiment backed by Mr Olmert.
"Our hope is that President Abbas and Prime Minister [Salam] Fayyad will be strengthened to the point where they can lead the Palestinians in a different direction," he said.
But there was no specific mention of how the US or Israel intended to address the reality of a Gaza Strip run by Hamas.
Reports ahead of the talks said Israel wanted to tighten financial restrictions on Gaza, denying funds to Hamas.
However, a spokesman told the BBC that Israel had no intention of stopping humanitarian aid reaching those in need.
The talks in Washington came a day after the US and the EU announced the lifting of a financial and diplomatic embargo on the Palestinian Authority imposed after the Islamist group won elections power 18 months ago.
Mr Abbas dismissed the government on Thursday after it seized control of the Gaza Strip. The factional fighting left more than 100 people dead.
On Monday, US Secretary of State Condoleezza Rice announced that the US would resume full diplomatic relations with the Palestinian Authority immediately.
She also announced $40m (£20m) of emergency aid to the UN Relief and Works Agency (Unrwa), which runs relief efforts in Gaza, now controlled by Hamas.
Israeli Foreign Minister Tzipi Livni also confirmed that up to $800m (£400m) of frozen tax revenues held by Israel would now be transferred to the Palestinian Authority.