President George Bush has warned US aid to the Palestinian Authority may be cut after Hamas' surprise election win.
He said the US would stop $400m (£225m) of aid unless the Islamic militant group renounced violence and stopped calling for Israel's destruction.
"If they don't, we won't deal with them," he told US TV channel CBS News. "Aid packages won't go forward."
There have been more clashes in Gaza between Hamas and Fatah, the party of Palestinian leader Mahmoud Abbas.
The worst of the trouble was in Khan Younis, where several people were wounded when Hamas activists exchanged fire with members of Fatah, which lost the election on Wednesday.
Hamas won 76 of the 132 seats in the Palestinian assembly and has the backing of a further four independent MPs.
But Israel has indicated that newly elected Hamas legislators will not be granted free access between Gaza and the West Bank.
The BBC's Richard Myron in Jerusalem said it means Hamas MPs in Gaza will not be able to travel to the Palestinian parliament in Ramallah in the West Bank, as they would have to cross Israeli territory.
Our correspondent says if Israel does chose to confine Hamas legislators to Gaza, it will make governing the divided territories even more difficult.
Aid in doubt
The Palestinian Authority has always been heavily reliant on international cash, and its main donors, the US, EU, Japan and Arab states, are reviewing their position.
"They've got to get rid of that arm of their party which is armed and violent and secondly, they've got to get rid of that part of their platform that says they want to destroy Israel," Mr Bush said.
The US state department said it would also be reviewing all US money given to Palestinians through the UN or non-governmental groups.
"To be very clear, we do not provide money to terrorist organisations," said White House spokesman Sean McCormack said.
Hamas is classified by the US and the EU as a terrorist group.
However, the EU, the Palestinian Authority's largest donor with $606m (£341m) a year, has so far not threatened direct aid cuts.
But a French diplomat quoted by news agency Reuters said a refusal by Hamas to give up violence would have consequences.
Meanwhile, Israel has cast doubt on its willingness to continue to transfer customs and tax revenue, worth $50m, collected on behalf of the Palestinian Authority.
"We will face practical problems of how you deal with people that call for the destruction of Israel," said Joseph Bachar, director general at the Israeli Finance Ministry.
But Mr Sinokrot said the authority would face financial hardship if Israel chose to withhold the funds, which go towards paying the salaries of some 135,000 civil servants.
"This is not donor money," he told Reuters. "If those salaries are not coming, this is a message for violence."
Hamas leaders appeared to remain defiant in the face of the donors' threats.
"The US administration and European countries should put pressure ... on the occupier and not the occupied and displaced Palestinian people," said Ismail Haniya, who headed the Hamas election list.
The US, UN, EU and Russia working for peace in the Middle East will hold talks in London on Monday.