The Quartet's words were chosen with particular care
UN chief Kofi Annan has said future aid to the Palestinian Authority will hinge on the government's commitment to peace and recognising Israel.
Speaking for the Mid-East Quartet - the EU, the US, Russia and the UN - Mr Annan said any new government must accept previous agreements.
Aid to the Palestinians has been thrown into doubt by the election victory of Islamic militant group Hamas.
Hamas has already rejected the conditions listed by the Quartet.
Hamas, which is designated a terrorist organisation by the US and the EU, said it was up to Israel to change, by ending its occupations of Palestinian land.
"The Quartet should have demanded an end to [Israeli] occupation and aggression... not demanded that the victim should recognise the occupation and stand handcuffed in the face of the aggression," Hamas spokesman Sami Abu Zuhri was quoted by Reuters news agency as saying.
The Quartet's statement, read by Mr Annan after a meeting in London, said: "All members of the future Palestinian government must be committed to non-violence, recognition of Israel and acceptance of previous agreements and obligations, including the roadmap."
It said future aid would be reviewed in reference to these demands, but did not threaten to cut it in the short term.
The BBC's diplomatic correspondent, James Robbins, said the words were chosen with care. They did not demand a renunciation of violence or immediate recognition of Israel, but a commitment to these things in the future.
The Quartet powers hope that by its actions, rather than words, Hamas can show itself willing to commit to peace efforts, our correspondent says.
Earlier, EU ministers made similar demands of Hamas, and said funding would continue as long as the new government proved it was committed to peace with Israel.
The EU is the biggest donor to the Palestinians, giving about $600m (£340m) in 2005.
Palestinian leader Mahmoud Abbas urged donors not to cut funding to ensure "that the institutions continue to function and the plan to build our independent Palestinian state is not disrupted or derailed".
Speaking after meeting German Chancellor Angela Merkel in the West Bank town of Ramallah, Mr Abbas said it was vital that the work of the Palestinian Authority should carry on as normal.
Mr Abbas also vowed to honour all peace agreements with Israel.
Hamas 'must change'
A senior Hamas leader, Ismail Haniya, promised all foreign aid would be spent on daily needs - not on attacking Israel - and would be subject to monitoring.
"We assure you that all the revenues will be spent on salaries, daily life and infrastructure. You can review this," he said.
European Union foreign policy chief Javier Solana said it could take up to three months for a new Palestinian government to be formed, and by then he hoped to see progress by Hamas.
"If these conditions are met then we stand ready to continue [to fund the Palestinian Authority]," he said.
"If [Hamas] do not change then it will be very difficult," he added.
1: Distributed through World Bank $85m
2: For Isr/Pal integration $12m
3: For UN relief (UNRWA) $77m
4: Food aid $35m
5: Humanitarian aid $33m
6: Special projects $24m
7: Infrastructure $72m
8: Other donations by member states $262m
EU TOTAL: $600m
1: Unused funds from 2003/04 financial year $175m
2: To pay PA debts $20m
3: Spending on new Gaza infrastructure $50m
4: USAID projects $155m
US TOTAL: $400m