This comes as Western nations threatened to cut off aid to the Palestinian Authority if the group does not soften its stance on Israel.
Hamas leaders said the aid cuts violate the Palestinians' democratic rights, but Condoleezza Rice, the US secretary of state, declared: "The principle is very clear: We're not going to fund a Hamas-led government."
Hamas has rejected Western demands to renounce violence, recognise Israel and accept previous agreements between Israel and the Palestinians.
The US and European Union list Hamas as a terror group, as does Israel.
Up to now the Palestinian Authority has received a large part of its $1.9 billion annual budget from overseas sources, and it may run into immediate difficulties next week when March salaries are to be paid for 140,000 government employees.
Rules of democracy
Ismail Haniyeh, the new prime minister, said on Thursday that the aid cuts hurt the Palestinian people.
"We were hoping that some countries would respect the rules of the democratic game and that they would have had different positions and not act this way," he said.
Mahmud Zahar, the new foreign minister, hinted that any country that shuns Hamas will be considered "an enemy of the Palestinian people".
Haniyeh hopes some nations will
respect rules of democracy
He said Foreign Ministry employees would not be allowed to talk to them, without listing the countries.
Rice said the US was reviewing its Palestinian aid programmes to see which ones it would need to freeze.
Rice said she expected to talk about Palestinian funding with France, Germany and Britain during her current trip.
"We've been very much on the same page," she said.
The Quartet of Middle East mediators - the US, EU, Russia and the UN - warned the Hamas-led government on Thursday to recognise Israel and seek peace talks if it wants to be guaranteed continued aid.
"The Quartet concurred that there inevitably will be an effect on direct assistance to that government and its ministries" if those conditions are not met, the mediators said in a statement.
Israel has stopped transferring tens of millions of dollars a month in taxes it collects on behalf of the Palestinian Authority.
Immediately after the new cabinet was sworn in on Wednesday, Canada announced it was cutting off donations.
"International law is the line of defence for the Palestinian people, and the fact that one country does not abide by it does not belittle these agreements' importance, especially for the weak"
ex-Palestinian foreign minister
Hamas officials hoped Arab and Muslim countries would fill the funding gap, but the Arab League summit this week ended with states only reaffirming pledges to provide the $55 million a month, a commitment they have rarely met.
Amid the threatened aid cuts, the new Hamas ministers assumed control of their offices on Thursday, sometimes in unorthodox ceremonies.
Ahmad Qureia, the outgoing prime minister, was forced to turn his Ramallah office over to Nasser Shaer, the incoming deputy prime minister, because Israel did not allow Haniyeh to travel there from Gaza.
Speaking in Gaza, Haniyeh said the seamless transfer was a testament to Palestinian democracy.
"This is proof that our people is a great civilised people, and the peaceful handover of power will now be a routine that our people will abide by," he said.
At the Foreign Ministry handover, the outgoing minister, Nasser al-Kidwa of Fatah, ended up in a debate with his successor about the need for the Hamas government to follow previous international agreements.
Zahar reiterated Hamas' stance that it would only abide by agreements it considered in the Palestinians' best interest.
Zahar (R) hugs former foreign
minister al-Kidwa on Thursday
"Why do we have to preserve these agreements frozen or mummified and then worship them?" he asked.
Al-Kidwa parried that international law and agreements were there to protect the Palestinians.
"International law is the line of defence for the Palestinian people, and the fact that one country does not abide by it does not belittle these agreements' importance, especially for the weak," he said.
Said Siyam took over the powerful Interior Ministry, which controls some of the Palestinian security forces, and insisted he would not arrest resistance fighters, one of Israel's conditions for peace talks with the Palestinians.
Siyam hinted, however, that he might to try to rein in the myriad armed groups by persuasion.
"We will not put our sons in prison, for political membership or resisting (Israeli) occupation, because occupation is the reason for the problem," he said.
US envoys Elliot Abrams and David Welch met Tzipi Livni, the Israeli foreign minister, on Thursday in talks that focused on the new Hamas government and the long-stalled "road map" peace initiative, the Israeli Foreign Ministry said.